If its looked after well - theoretically as long as you need it to last. Although it depends on your uses now, and in the future, maybe in 4/5 years time, there'll be some super-cool must have laptop technology that will render your macbook past it - but it'll carry on doing the basics for a long long time!
I have an iMac G4 from 2002, so that's a testament on how well Apple machines hold up over time. It's a little slow but still chugs along running pretty damn well for a 9 year old machine. As for your MacBook, I just bought the same model MacBook off eBay and they are great machines. Mine is just under 4 years old since built and it's pretty solid. It was previously owned by a school and it has some dings and some marks, but for $400 I sure can't complain. Just enjoy your MacBook and take care of it and it should last you for many years to come.
Have owned Macbook 13" from new - Dec 2006. Took out 3 yr warranty. Have had logic board replaced twice under warranty (normally $900 Australian). Paid $350 for new hard drive and battery 6 months ago. Logic board just died again and repairer wants $900. Our Macbook hasn't been dropped or damaged at any time. In my experience, beware!!!!!
It's hard to say due to the fact you bought it used & may not know it's true history. I've had lots of Mac laptops & until the last few years, they were long lasting.
Recently Apples pushing so hard to dominate, it's reflecting in both quality & longevity. I've had 2008 & newer show declining quality and bugs or issues one had not seen in macs of the past. Unfortunately my 2009's & newer (I buy mine new) have been fraught with problems.
I don't see anything to indicate this trend will not continue, and frankly that's very discouraging to someone who likes them as much as I do. It's also important to note I am very careful with mine & know how to maintain them.
In the last year or so Apple is so obsessed with it's mobile OS, the computers seem to be a secondary consideration.
Well, I just thought I'd give an update, in case anyone cared (or was in a similar situation).
I've had my macbook a week now and it's working great, almost like a new macbook. The fan does get a bit loud when running flash applications, but the noise doesn't bother me too much.
I'm planning on upgrading the memory, so I'm excited about that.