Personally I wouldn't bother but that's me. I'm not sure I get this apparent need to lounge hop but if that's what the OP wants ...
You'd need to allow time to get to T3 (which involves clearing security on arrival at T3) and then as stated in the second link posted above 90 minutes before departure to get back to T5 (and again reclear security)
The poster in the second link @
corporate-wage-slave is a denizen of LHR and he probably knows more about getting around it that many of the staff there so if he says 90 minutes then he means it!