Sorry so late but I'm an habitual rewriter.
Angelique, are you aware DARPA has debuted the world's first functioning guided rifle bullet? There have been a few commercially-produced shooting systems billed as "guided," but that was largely puffery referring to a highly computerized and automated aiming system. The DARPA bullet actually
steers itself in flight, same as a guided anti-aircraft missile. Conceivably, that development could change everything. And it's not Buck Rogers, it's here and now.
As to your specific questions, seriatim,
How far is too far?
This could get crazy involved, so let's keep it as near to practical and as far from theoretical or philosophical limits as possible.
I suggest you consider
this Wikipedia page listing the longest known sniper shots. Because these are records of real-world shootings, they represent a practical convergence of the limits of rifle accuracy and lethality.
One point I find especially telling is that over a period of 42 years, from 1967 to 2009, the range of the longest known sniper shot only increased by about 8%, from 2500 yards to 2707 yards. This is remarkable on a number of fronts, beginning with the fact that there was no formal sniper training until the Vietnam war. So despite 40+ years of of formalized sniper training, despite the advancements in rifles and ammunition following the advent of computer-aided design and manufacture, computer numeric control machining, and computational fluid dynamics, and despite the fact that the latter decade of that period was marked by the simultaneous prosecution of two of the longest wars in American history, with countless of sniper shots taken at tremendous ranges and at elevations in excess of one mile, 8% is all we've got to show for it.
Clearly, by 1967, the art of creating a bullet that will fly with almost perfect regularity had reached a plateau. So barring some earth-shaking new innovation (such as the DARPA self-guided bullet), I would expect to see roughly the same rate of advancement (about 0.2% per year) for the foreseeable future.
Which leads me to suggest that, provided your target has near-human physical vulnerabilities (a matter not yet addressed), these numbers are the sign post marking the approach of "too far."
By that measure, 5000 yards is nearly twice too far.
What would you keep in mind for a trajectory inside a city?
The laws of physics do not change when you pass the City Limits sign. If by "city" you mean towering buildings and concrete canyons, the most notable change is the buildings will alter wind direction, canalize it and create turbulence. Which could introduce localized wind currents that affect the flight of the bullet but do not reveal themselves to the shooter.
One potential structural problem is above-ground telephone and electrical power lines. At the kind of ranges you're talking about, the bullet will travel in quite a tall arc, raising the possibility of it clipping a utility line in flight. You might want to select a location with no above-ground lines, like NYC.
Mirage or heat shimmer blurs optic's imagery at extended ranges when cooler air overlies sun-heated ground. The fact that the concrete canyon serves to limit the incidence of direct sunlight means this probably will be less of a problem.
What rifles are out there today?
Any rifle on the Wiki list I linked to above has a CV suitable to your needs, although one or two might be too esoteric to suit.
I might be ill-informed but I am unaware of any military organization using Cheyenne Tactical rifles, or any of their Chey-Tac branded cartridges. Which is no indictment, either of the quality of their rifles or
the capabilities of their cartridges. There are any number of other reasons why a perfectly suitable weapon might not be adopted by any military, not the least of which is that military procurement systems pretty much the world over tend to be rather byzantine. Or corrupt. Or both. Which doubtless dissuades some companies from getting into bed with them.
In separate references you've mentioned Chey-Tac and their .408 cartridge, so I gather their rifles have piqued your interest. It might not carry the same brand-name recognition as some of the other weapons, but from a pure performance standpoint, provided the range is plausible, I think it would be well-suited to this application.
We don't let zebras wander the streets in America, so I surmise from the 'zebra crossing' reference that you are British (or whatever country you do hail from still puts QEII's image on their money). So I also presume this book will be targeted to an international audience. As it happens, the sniper who made the current record 2707 yard shot also is British. His rifle was the British-made Accuracy International AWM (designated the L115A3 by the British Army), chambered in .338 Lapua Magnum. His bullet of choice was the 250-grain Lapua Lockbase. Selecting the same equipment for your shooter should give it the ring of familiarity to your international audience, and affords you a bit of flag-waving. In some circles it is regarded as the finest sniper's weapon in existence.
But one caveat. The war in Afghanistan primarily is conducted high in the mountains. I don't recall ever having seen the firing elevation on that shot, but at least a mile is a safe guess. Thin air lets the bullet fly faster, farther. At that extreme distance they reached their target with barely more energy remaining than a pistol cartridge fired at close range. At lower elevations, the lethal range would be a fair bit shorter. The British Army lists its maximum effective range as 1,640 yards. 2707 was pretty miraculous. Yet despite that, once he'd found his range, the marksman scored three consecutive hits (two on the Taliban themselves and the third on their machinegun)
OTOH, I wouldn't kick a McMillan TAC-50 out of bed for eating crackers.
Would it be possible to take a shot using a live satellite feed (provided you have access to that) instead of a scope?
Does different scopes have different range limits, or how does it work?
Films wildly exaggerate the capabilities of spy satellites, especially as regards this "live feed" function. But very few people ever have been in a position to learn the truth of it, and most of the cinema-going public already has been brainwashed by the myth perpetuated by the likes of Jason Bourne and Tom Cruise films.
If you use it, it isn't realistic, but those who would know are few and far between. On the other hand, traffic cameras and police CCTV cameras are quite common in modern metropolitan areas, and are imminently "hackable."
As to the scope range limit question, the marksman has two methods for compensating his point of aim for bullet drop due to gravity at range. The scope itself provides one of these in the form of elevation adjusting turrets. Twisting the turret to the desired setting physically moves the crosshairs up or down a tiny amount within the scope. Up for a lower point of impact, or down for a higher POI. Because the inside of the scope tube is of a finite size, so is the amount adjustment available through the repositioning of the crosshairs.
Which brings me to the second means, which is simply hold-over. If the shooter's scope has run out of vertical adjustment range, or if he chooses not to employ it, there's nothing stopping him simply aiming at a point in the air a certain height above the target. In fact, all sniper/military scopes feature graduated markings on the crosshairs themselves to allow for a precise hold-over.
I earlier deliberately didn't address your question regarding hitting a moving target. I did that because I thought it better left for here.
Those same graduated markings on the scope's crosshairs can be used by a shooter skilled in their use to calculate (and aim with) the precise amount of lead needed to hit the moving target.
This is known as a Mil Dot reticle. It also is the sniper's Swiss army knife, the tool of a thousand uses. Before you finish the book, I suspect you will become quite intimate with it.
The distance between the center of any two consecutive dots is one millirad, one one-thousandth of a radian. This is a rather arcane measuring system but it enables dimensionless measuring. If you scope a cricket bat, and it happens to measure exactly one millirad tall (or 1 mil, for short), you know it also is exactly 1000 bat lengths away. That's the whole point to (and magic of) the mil. If you also know the maximum allowable length of a cricket bat is 38", now you also know the bat is question is at most 1056 yards distant.
Snipers commit to memory the dimensions of as many common everyday items made in standardized dimensions as their brain will store; house exterior doors & windows, car wheels and tires and number plates, street signs, letter boxes, drinks cans. Even the dimensions of the average bodies of the native population; overall height, waist to top of head, width of head, width of chest, length of walking stride, length of running stride. All to allow them to almost instantly measure range to target, and gauge speed of movement, all in their head, all without electronic aids.
If you need more detail on scope construction, read
here. The bits directly addressing your questions are about 2/3rds of the way down, adjustability.
What would happen more specifically if you're hit with a .408 caliber?
Handloaders load ammunition to their own personal specifications to suit their particular performance needs. So the shooter is not confined to factory-manufactured ammunition. The military operates somewhat similarly, but their bullet selection is limited to those deemed not in conflict with the Hague Accords, which prohibit the use in warfare of bullets that might cause undue suffering, an artifact of the soft-nosed lead bullets once made by the British in a place in India called Dum-Dum. You might have heard of it.
As for the extent of damage the bullet would cause, that factor is near infinitely "tune-able." Some bullets are designed to cause highly localized, explosive terminal effects. Some are meant to strike a balance of penetration and expansion, distributing the damage over a longer trail. And still others are designed to provide pure penetration with negligible expansion, hoping to reach some heavily-armored or deeply-buried vital organ. And that's painting in broad strokes. Almost any bullet performance niche you can conceive of, either there already is someone building it, or there's someone who can and will, ...for a price.
