Hinton's P-51 Voodoo has done passes at more than 550mph with a single piston engine, so that turboprop still has more to master.
Some claims for aircraft performance can have really strange answers. For example, with no engine at all, the Perlan project glider recently went to 74,298 feet (gps altitude), higher than the record of the Lockheed U-2 subsonic .jet spyplane. Their project goal is 90,000..