Daniel, first of all, I'm jealous of your predicament. That said, I think you've gotten some good advice already, so I won't repeat what's been said. But I will throw out a few ideas that haven't come up. My first thought is that you may be underestimating upcoming expenses. It sounds like your current expenses are low, and that's great! I'm impressed that you're living below your means, and looking for the best way to use your extra cash. But you may not be thinking of a few things.
You have a girlfriend, and maybe your relationship isn't such that you are planning a wedding quite yet. But, regardless of whether your current girlfriend is your future life partner or not, if you think marriage may be in your future at all, you'll save yourself a lot of stress if you've got some savings for a wedding in place before you're ready to commit.
Next, what are you driving? If it's a good car that you expect to last you another 10 years, you're probably ok right now. But if you may need to replace your vehicle in the next few years, start saving now and you may be able to buy it outright. (I expect your interest rate on financing a car would be higher than your current student loan rates, so I would save for a car before paying down loans with such beautiful rates.)
A house has already been discussed, and there was also mention of additional education, and both of those require a solid financial plan that begins far in advance.
In summary, I think you need a lot more than $5K in savings. Sure, have some fun, and take advantage of opportunities to travel, etc, as they come along, but if you're able to bump your savings by $500 to $1000/month, I think you'll really be glad you did. When it comes time for a new car, or you find you're ready to settle down, it will be nice to have somewhere to draw from, and if there's only $5K in your savings, you may come to regret choices you made when you were 22.