How long - exactly - do your gmat scores last?

GMAT scores last five years from the day they're taken, so you have to submit an application within that five years. The point at which you actually begin classes isn't fixed by your GMAT score; only the date by which you have to submit an application is. What impact that has on your enrollment will vary by program. Keep in mind, though, that if you're planning to use scores that are 4 years and 11 months old or something, some programs may ask for more recent scores when you get around to applying.

Does that mean I am actually at a disadvantage if I plan to take the gmat now? Is it enough of a disadvantage that i should just take it a few years down the line?

And also, how do I actually find which programs are actually affected negatively by this?

Thanks!

That depends entirely on which programs you're looking at. Some of them will be happy to take a score that's nearly 5 years old, and some will want to see something more recent. Some schools will, as you asked initially, even require that your GMAT be within 5 years of your enrollment, but that's entirely at their discretion. The only way that I know of to be sure is to contact the admissions departments at the schools you're interested in. They're used to answering those kinds of questions, so it shouldn't be a big deal to make a list of some target schools and then make some phone calls or email inquiries.
I think it's actually a good idea to take the GMAT right out of undergrad, since you're used to studying and testing, and your math skills are probably still in good shape. A lot of people find that, after a few years out of school, their math has gotten rusty and it's an uphill battle to regain those skills, which makes the testing experience a challenge. If you have time to prepare properly now, it can't hurt to take the test, and it might help you in the long run. Just be aware of the possibility that you might have to retake it somewhere along the line if a school requires you to get a more recent score or if your score isn't up to par at the schools you're looking at.