Yes it is an airside bus at T3 Flight Connections to T5. The bus journey takes 11 minutes, and the service frequency is every 6 minutes, depending on the time of day. I've done T3 to T5, gate to gate, several times in under 45 minutes, though an hour is more usual. The security scan will be at T5, so that's the bigger variable, but you have fast track (which is along the wall on the right) or the option to go UK Border and up via South Security, if non EEA passports doesn't look too bad.