It is difficult to find examples with more than 3 forces, let alone 5!
An airplane in level flight has 4 Obvious forces...thrust, drag, weight and lift.
If you felt it was OK to include lift due to buoyancy I suppose you have 5 forces!!!!!!!
OK - draw a picture of a person with five arrows pointing off them.
Maybe the person has been lassoed by five other people and they all pull in a different direction to hold the captive still?
Tie a rope to each limb, also tied to a horse each ... there's 5 forces: tension in each rope, and gravity.
Perhaps the person is seated at a computer, and there is a cat sitting on his/her lap with all claws slightly extended in affection - that's five forces: gravity/chair and one for each set of claws :)
Arctic wolves count?
Diagram shows 5 arctic wolves pulling on a carcass.
... what is this for anyway, that you cannot google "five force statics"?
No, otherwise, the block wouldn't go up the incline. The pushing force must exceed both the friction and the "tension" and the gravitational force in the parallel direction (perhaps tension is not the best words, it's the "push back" from the rigid rod).
Ah - it's the "bottom" block you are considering. (You are right, "tension" gave me entirely the wrong picture.)
it gets the push-back from pushing the top block, drag from friction, weight, normal-force, and the actual push. That's 5. Good call.
To fit the criteria - the block should be held stationary or moving at a constant speed, of course ;)
There's quite a lot - for eg. an aircraft could get thrust from more than one engine, giving more than 5 forces; a car parked on a slope has 4 normal forces, and four frictions (each tire), which would be especially important if there were an uneven mass distribution. Also take into account the springs in the suspension and it gets as complicated as you like.
If the thing has to be at rest, perhaps my example is not the simplest because the friction force is variable (keeping the thing from moving), so it's not easy to tell which direction it points right off the bat, depending on how strong the pushing force is.
You have static friction - no worries.
In analysis you just pick a direction and if you guessed wrong, the friction force will just come out negative.
(There would be two static solutions, one where you push against friction and the other where you let friction take some of the weight.)
... of course stationary, the blocks could probably just get treated as one.