V-Flyer

how do you get between T5 & T3 if you have to collect baggage & aren't using flight connections?

HEX or Heathrow Express, it's free between the terminals too and many say it is the quickest way (even over flight connections).

As Slinky says, use the HEX. The T5 station is the very bottom level of T5, underground. The HEX takes about 10mins and drops off at the underground central station area which is about a 15 minute walk to T3 departures.