I have a 130i E87 (same engine) which cost £3.5k and its bloody fantastic - I think 265bhp and I can't imagine needing anything faster... I have the Street Triple 765 if I want to go really fast!
The N52 is something else - not sure if I can put my finger on why its so good?
Think you’re going to struggle to get close to £5k without entering potential bork territory. This might be worth a look though:BMW 135 m sport coupe.
Entry point for M135i is still £12-13k