Five years is plenty of warning to do *something*. Whether a mass driver could be designed, built and launched in time is questionable. Maybe with full global resources it could be.

Nuclear weapons would definitely work if used in a stand off detonation. It simply needs nudging off course. In space there is no atmosphere, hence no blast wave -- just heat and radiation. A stand off detonation would vaporize a layer of material, nudging the asteroid the opposite direction.

Existing ICBMs can reach escape velocity if stripped down to one warhead. The existing warhead "bus" already has substantial maneuvering ability. It would only need an additional guidance package to enable a precision stand off detonation. That could be ready within weeks.

One problem is the warhead is "only" 300-400 kilotons, so likely multiple shots would be needed. However there are 50 Peacepeepers and 264 Trident II D-5 missiles available, so multiple shots would be possible. The Russian force would presumably also be available (it's a global problem).

Much larger warheads are available, up to 20-50 megatons and launchers could lift those if necessary but it would take many months to get ready.

A high confidence approach would be needed, as a 10 km asteroid impacting at 17 km/sec (a typical speed) would be equivalent to a 54 million megaton bomb. It would destroy any structure within a 1500 km radius, and would probably cause drastic climate changes.

5 years at 17 km/sec puts the detection distance at 2.68 billion km (roughly the orbit of Uranus). From that distance it would only require deflecting 1/2 arc second. If intercepted about halfway to Jupiter (1 billion km) it would still only require 1.31 arc seconds deflection.

You obviously want to deflect it as early as possible, not wait several years for the best possible technique.

A 10 km astroid is 510E9 cubic meters. If composed of dense rock (3000 kg/m^3) it would weigh 1.53E15 kg. If detected at 5 years out, and deflected at about 2.5 years out (roughly 1 billion km), it would only require 8 cm/sec lateral deflection. This would require 4.89E12 joules or 1.35 gigawatt hours energy. Probably a mass driver could do it, assuming it could be designed and built in time, along with the power source and booster. Nukes could easily do it.

Considering the entire world would be at risk, you'd probably want multiple parallel approaches to ensure something worked.