To get from Terminal 5 to Terminal 3, simply go the terminal's mainline rail station and hop on a Heathrow Express train. They run every 15 minutes, with a journey time of about 3 minutes. No ticket is required, as travel between terminals is free of charge.
If you'd rather take a bus, services 441 and 724 run between the two terminals, taking 10 and 20 minutes respectively. At night (2355 to 0455) the N9 bus does the journey, taking 10 minutes. Once again, inter-terminal travel is free of charge. (Terminal 5 has its own bus station. Terminal 3 is served by Heathrow Central bus station).
Chris