If you spotted a an extra-terrestrial object five years out that could destroy Earth, it would be an asteroid, not a comet. Comets come in really quick in comparison to asteroids. The biggest of them can do a lot of damage, but they are generally not planet killers. They are smaller than asteroids and they are made up of mostly dust, ice and carbon monoxide, which is why they usually dissipate in the atmosphere.
Asteroids are the potential planet killers. They can be much bigger and can be made up of metals and rock. Fortunately, they are easier to see coming and track. The one that we know of that has the greatest chance of impacting Earth is designated 2009 FD. It has a 0.2 percent chance of hitting the Earth in the year 2185 - 2198 timeframe. I’m not going to get my panties in a knot about it.
Also, why would (no offense) we amateurs at CAF be tasked with dealing with it? Wouldn’t NASA or DoD or the UN Security Council be preferable? I get that it is a hypothetical, but some hypotheticals are so ridiculous they are not worth much discussion.
There are rough plans to deal with asteroids. The most likely is to send two unmanned spacecraft to the asteroid. The first would be a scout. It would follow the asteroid and determine precisely what its trajectory is. It may determine it is not really a threat. If it is a threat, the second spacecraft would contain a thermonuclear bomb. The detonation would not be to destroy, but to knock the asteroid off course just enough to miss the Earth. We would have years to work out the details.
