For the case of Y-30 and re-engine of the KJ-600 and AG600M - It's not so much about speed, but much more about the weight of the aircraft.
A more powerful turboprop engine would deliver more shaft power to drive the propellers, meaning greater amount of thrust can be produced to drive the aircraft forward per engine. This means that more powerful turboprop engines enable heavier aircrafts to be propelled into the air.
This is crucial for the case of Y-30, if significant step-ups in overall size, cargo hold size and payload capacity from the Y-8/9 are to be expected.
That's also why the C-130J with ~70 tons of MTOW requires 4x ~3500kW turboprop engines, whereas the A400M with ~141 tons of MTOW requires 4x ~8200kW turboprop engines, i.e. more than twice the amount of power per engine for about twice the MTOW.
Apart from that, there's also the case of enhancing hot-and-high and/or short field takeoff and climb performances with more powerful turboprop engines. This is similarly important for the PLAAF with regards to operations on the Xizang Plateau and the South China Sea islands (and also for the case of the PLAN, should they need the KJ-600s to operate from the STOBAR twins.)
So, yes - 5000kW turboprop engine is a real necessity.