Hi. I'm a final-year undergrad and I've been offered doing a PhD at the university which I'm currently at with a studentship of £5,000. Would this be enough?

Well you tell us, you live there already! Assuming the 5k excludes tuition fee payment, then that would be scraping the barrel for living costs i'd imagine. Its feasible, especially if you could supplement it with part time income

If you are in London or travelling to London I dont think thats a very good offer, but if you can cut rent or travelling somehow probably (for a month it will will be around £400..although you will be paid quartely).. do the budget,ask someone who had done it in your uni..with same amount.

A lot of non-London places estimate around 8-8.5K as living costs for the year. I had a studentship around this amount last year and lived reasonably okay on it. 5K would probably be very tight, but again, depends where you are and your lifestyle.

£5K is nowhere near enough to live off if you want your own place, but if you're happy to flat share then that's ok.