If your luggage is not checked thru you would need to go thru immigration (quick if you have an EU passport, otherwise could be much longer), then wait for your luggage, take it to the Heathroiw Express station (quite a walk), wait for the train, quick train ride, walk to T5 check in and check in there, then go trhu security and immigration again.
With access to the premium lines, priority bags etc you should be in the lounge in around 90 min after deplaning if things go reasonably well. With long lines it easily could be far over 2 hours.
Could you connect somewhere else?