Rockhopper’s link is a little out as that is industrial gas turbines, and the shaft speed quoted is, I think, the shaft speed of the free power turbine which would then drive the pump/generator/propeller shaft.
It is a bit complicated due to all sorts of aerodynamic jiggery-pokery. Rolls-Royce engines are 3 shaft – low, intermediate, and high pressure systems. GE & P&W used 2 shaft.
It’s been a few years since I left RR, but from memory the Trent500 at take off would be running the LP system (ie the front fan & LP turbine) around 3000rpm, the IP system around 8000, and the HP system 10,000+.
I’m sure someone a bit closer to the action will be along shortly and correct me if I’m way out!
Rob