Is there an easy way to remember the 5 steps of the problem solving cycle?

You could use a mnemonic for IPDRA. But to be honest, for something this small, once you've learnt it, and more importantly understood it, it'll be hard to forget.

If you have a problem, what do you need to do?

Identify it - Otherwise you wouldn't know what the problem is

Plan - The best way to tackle a problem is to come up with ideas and a plan

Do - Do the plan, else you won't know if it works

Review - How did it work? Did you get the solution?

Adapt - What did you learn, would you change anything next time, were there mistakes, anything that went really well?

I do run sessions on memory training if that is of interest but for this, none are really needed.

Following your intuition would give you the majority of the steps.

1. Read the problem
2. Make a plan (this is the part most forget!)
3. Enact the plan
5. Solved and checked!

In an ideal world, step 4 (monitoring) wouldn't be necessary because you'd solve the problem without any issues. Monitoring is a good way to check you are on track to finding a valid solution.

As with remembering anything, it's incredible how helpful creating an acronym for it, or using the 'method of loci'. For the acronym way, say you need to remember 'Define problem, Gather information, Suggest possible solutions, Evaluate ideas, choose one', this becomes DGSEC, make up literally anything that you will remember for this (e.g. Do goats scream each centrury?) and your mind will do the rest. With the method of loci, picture your house, your classroom, anywhere in your mind and mentally allocate each of the 5 steps to say 5 drawers in your kitchen, now when you want to remember the steps, visualize looking in each drawer and whatever you 'stored there' should pop up in your mind.

You can think it as 2 parts : 1st part about problem which has 2 branches : identification and analyzing the problem

2nd part is about planning which has 3 branches:

develop

İmplement

And Evaluate the plan.

I hope this will be helpful for you