I am planning to get a Yaesu FT2900R 2 meter rig for my 2001 Honda Accord. With my 5w FT60, I wasn't able to reach repeaters that were any more than 10 miles distant (I live among mountains.) How far can I reasonably expect to get with 75 watts and a mag mount antenna?
It's hard to make guesses about this sort of thing because there are too many different factors. The mag mount antenna certainly is better than your FT60 antenna, and the 75 watts is certainly better than the 5 watts - but how much is subject to a number of factors. To get a good guess you can use that doubling the range requires four times the power (which is equivalent to a 6dB gain), and accounting for your increase in power (15 times power = about 4x range) and the better antenna (depends on the antenna).
There are quite a few other factors involved. For example, the 75 watt radio probably also has a better receiver than the HT, and may be able to discern weaker signals - on the other hand, while the increased power may get your signal out much further, it has no effect at all on you being able to receive signals. The only factor that improves both TX and RX is your antenna gain.
Determining radio range is very difficult if not impossible to do. There are loads of factors that will contribute to it and it's not something that can be easily quantified or predicted.
If you have mountains in the way blocking signals, no amount of power will help. That said, if the mountains, cliffs or ledges are arranged such that you might actually get some reflection, more power could help by increasing the amount of reflected signal that makes it to a repeater.
Certainly, if you are going from an HT with a rubber duck antenna, going to an external and larger antenna is the most effective step. Adding power can't hurt though either.