Personally, I'd wait a bit just to make sure he likes it and sticks with it(but I'm cheap, lol). With our two older ones, we rented cheaply at first (violin and cello), then went to a nice rental violin for older dd, then bought one. Ds10 is starting band/orchestra (he's still in instrument selection mode) and I plan on renting from a preferred vendor to get basic quality but NOTHING extravagant. Of coure, unlike the dds, he has next-to-no musical ability, so I don't want to spend too much.
I honestly just don't think a 5th grader will sound that good no matter what. OTOH, I did think private lessons made a HUGE difference with the dds (we did voice, cello/violin and guitar for one dd). You will have a pretty good idea within the next six months of what level of player your son will be... not perfect, by any means, but just an indication if you will need a "serviceable" instrument or if it is worth a bit more.
Good luck!
Theresa