On our return, we arrive at LAX at 8 am on a Friday morning from Cairns/Sydney.
Any suggestions for 5 hours in LA until our next flight at 2 pm?

You will be EXHAUSTED so suggest you use one of the many Airport Hotels most of which have a free courtesy car and several have special "half day" rates. eg Holiday Inn (book on the Web) and even cheaper try the Super 8 Motel on Airport Boulevard.

We had a similar problem in LA - 8 hours between connecting flights. Don't underestimate how long it will take to check in and get to your gate, the queues were horrendous and it took us a lot longer than we had expected. We ended up catching a cab to Venice Beach, took about 20 mins, and had lunch and a walk. It wasn't very lively mid week but still good to get some fresh air and get out of the airport which is a bit depressing. We had thought of getting a day-rate at an airport hotel but were worried we wouldn't sleep as we'd be so concerned about missing our flight - you know how you check the clock every hour?
If you do a search under LAX on the USA forum, you will find other suggestions.
Kay

We took a city bus to Santa Monica and Venice Beach - at the time a very reasonable $0.50 each way. Better than hanging around the airport.

Not too familiar with LA geography overall, though - would the Getty Museum be a realistic option?

Considering the limited time available from arrival to check-in for the continuing flight, you haven't much time. If you venture too far (yes Getty Museum is) you run the risk of dreaded LA traffic problems. The nearby beach communities are refreshing, but if you compare them with those in OZ, you're going to be disappointed. Most of the rest of the area surrounding the airport is blighted, and some downright dangerous. Southern California is a wonderful tourist destination (I lived there more than 30 years of my adult life); save the experience until you have time to enjoy it.
Bigarm1's suggestion is the one I'd choose.

Depending on the 'security status' in the US your time may be spend moving from 1 lineup to another. In October our flight from Auckland arrived early (8:30am). Our connecting flight to Toronto was at 1pm but there was also a 10am. However, due to hightened security at LAX it took until after 11am just to get through the various 'immigration' & 'connecting flight'.

And even though our luggage had been checked through to our final destination we needed to collect all checked luggage for immigration & once through immigration the luggage needed to be rechecked (rather than just put on a 'connecting flight' belt, as it was checked in at Auckland) & everyones checked luggage was being hand searched.

So needless to say we didn't catch the 10am flight and once we grabbed some lunch and a couple of newspapers (as we had been away for a few weeks) it was soon time to start boarding.

Z

As an LA Native, I hate to tell you that the Getty would not be a good option as you would need to go over the dread "Sepulveda Pass" otherwise known as Satan's Flaming Lips.. to those of us who have to drive it from time to time.
A trip to the nearby beaches isn't a bad idea. One other note on areas near Airport, honestly they have come a long way since the 80's 90's and have seen a great deal of urban renewal they are not quite so blighted as they once were but unless strip malls and gas stations are your idea of a good time, you might want to stick to Venice Beach.

I'd go with the sleep option myself.

But if you'd like to go to a less touristed beach (and in my opinion, a little less nutty), hop a cab and ask to be taken south on Sepulveda to Hermosa Beach. Ask to go to Pier Ave and be dropped off at the end. It's a pedestrian square, and slightly off the square is "Good Stuff"...not a bad place for some breakfast. Cabs aren't too hard to catch in Hermosa (there's a spot where they line up), but you could always have them call one for you. I'd only do this if you have at least 2.5 hours from start to finish. So consider how much time you'll need to get in and out of the airport. Enjoy!