If it's all one ticket, you won't have to worry. When you check in at Perth airport, they should check your luggage all the way through to Leeds, as it's one ticket, but check with them that they do. The baggage tag receiptss you'll be given will then show them as going to Leeds.
On arrival into Heathrow, follow the Purple "Flight Connections" signs, then "Flight Connections Terminal 5". This will lead you to a bus to T5. When you get to T5, you'll then follow "Flight Connections UK Domestic", which will take you through UK Immigration. Then it's up stairs and through security, and into the terminal. If you don't already have the BA boarding card, there's a BA connections desk just before immigration who can issue it to you.
When you get to Leeds, you'll collect your bags, then exit the baggage claim area, probably through customs. (I'm not completely certain how they do it in Leeds). If you need to declare something, there should be a customs phone there, assuming there's no customs people manning the "something to declare not from the EU" line.
If for some reason your flight is late, the cut-off at Terminal 5 is to go through "conformance" (just before the immigration) 35 minutes before the flight departs. If you miss that, you go to the BA flight connections desk, who will re-book you onto a later Leeds flight. If you miss the last one of the night, they'll sort you a hotel too. Note that this is only because you'll be on one ticket, if you booked it as two different tickets you'd be out of luck...