T-28 pilot reported a taxiway excursion while attempting to exit the landing runway at an excessive speed. Pilot tried to accommodate an ATC instruction to exit the landing runway and locked the brakes in effort to do so.

Narrative

ZZZ Tower cleared me to land on Runway XX. I landed the aircraft as mentioned earlier; and ZZZ Tower instructed me to turn right on taxi 1. I proceeded to turn right into the taxiway 1 when I noticed that I was not at the proper speed. I locked the brakes as I turned into Taxi 1; but the aircraft skidded to the left; and due to the turn's momentum; I could not make the complete turn. I stopped the aircraft immediately. The nose of the aircraft got into the grass of the taxiway and was near the taxi light pole. I turned the aircraft engine off immediately. I advised ZZZ Tower of the situation; and they sent 2-people from the airport flight operations to assist. Flight operations were able to get 3 additional people; and we pushed the nose back into the blacktop taxiway 1. I started the aircraft; advised ZZZ Tower; and they cleared me to taxi back to my assigned hangar. No damage to the aircraft or to the airport. The aircraft was inspected; and no deficiencies were found. I was trying to comply with ZZZ Tower instructions; but I understand my mistake; and I should have reported being unable to take another taxiway. Nothing follows.