If you were to head to T3 immediately on arrival from LAX you would likely be fine, but you should plan for the transfer to take at least 45 minutes in each direction. You'll need to familiarise yourself with the T3 Airside exit route though, in order to return to the arrival flow. This way you won't have the "Ready to Fly" marker on your boarding card, and will be able to proceed through Flight Connections at T5 afterwards.
This is exactly what I plan to do in September, I have a 9 hour connection and while I plan on heading out of LHR a trip to the CX Flounge for some breakfast/noodles is rather appealing!