Make it a game. Pick up all thing that are green. Pick up something that’s soft. Throw 5 things in the basket. Who can pick up the most things in 30 seconds.

They sound overwhelmed if it's that bad. Take them shopping for storage options, then sort through it together. Teach them how to live, how to organise. Xx

My kids are similar ages. I find that they get overwhelmed with the mess and just don't know where to start so they don't bother. For me taking one child at a time to their room and literally sitting down with them and pointing to a toy "pick that up" pointing to where you want them to put it "put it there" and just showing them how to clean up, seemed to help. It's time consuming initially and takes forever the first few times, but after a few times you just go in and start them off pointing to a few things to show them how to start, then asking them to keep going and they'll do it on their own.
You and I know what we mean by "clean up" but as silly as it sounds, kids don't actually know HOW to clean up, unless you show them. And the bigger the mess the more overwhelmed they get.

My 5 cats sometimes drive me nuts

As someone said they are bored.
Give them limited toys and easy storage. You might have to nag and stand over them a bit but slowly they will get used to putting stuff away.