Your best friend is a 'post hole digger'...easy peasy, definitely will get you huffing and puffing a bit. It will be 8" wide and as deep as you are able. Should do fine working around stones as big as one's fist, if not, then a shovel is necessary.
If you run into a tough horizon in the soil you should have at hand, nearby, an iron pry bar (5' by 1 1/4" caliper) or a pick axe. $30 might rent a post hole digger. Use a tarp for soil you pull out of the holes. Great for new plant beds or your compost pile. Don't dump rocks next to the fence as they will cause rot as well.
Please send pictures...
3' deep is as deep as I know anything needs to buried. 5'? Even Alaska is 3'. I need to know what you are putting in those holes...
What material are your posts?
What are you thinking for fill material? Rubber chunks, bad idea, very very flammable. Bark chips lots of splinters. Pea gravel is best. Ensure drainage below the gravel before the landscape fabric is installed beneath the pea gravel. NINE inches of pea gravel is recommended for play structures.
Where do you live? If you live near a 'green belt' do not DO NOT put your play structure near a greenbelt. There ARE cougar, bobcat, bear that are watching for cats, dogs and little kids...even big strong athletes... that inhabit those greenbelts looking for food. Keep your play area right next to your home. Visible at all times. Vary your routines.
Where is it you live? tell us more about your situation. You will need pressure treated posts 4X4 and sonotube 10 to 12" in diameter, mix by hand bags of concrete. Depending on the structure you are building you should think about using post anchors at the top of the concrete in the sonotube. I would still use pressure treated lumber.
There is a super duper U V enhancer and wood protector that allows the wood to turn dove gray uniformly. Or make sure of the toxicity of the paint/stain. Pea gravel was all I would use for safety and expense.
Are you getting a kit for this play structure? What are their recommendations and why would you be supplying the posts? That must mean this is your design, way cool...? Landscape fabric on soil after graded for drainage (somewhere else) The square footage divided by 81 gives you yards to order to get 4" of fill. You will need to double the yardage for 8"...some insurance agencies demand the 9" thing for what I don't remember.
Don't use your fence as a boundary, causes problems mostly rotting your fence. Keep the play area right next to your home.