きます、はきます、します、つけます、かけます

What is the one English phrase that can be used for all of the above 5?

The answer is to “put on”.

Let’s revise the difference among the 5 words.

きます for clothing items for the upper body or the whole body (dresses, suits, etc.)

はきます for clothing items below waist and footwear.

します and つけます for accessories such as a ribbon, a tie, etc.

かけます for glasses.

The reason why they are to “put on” instead of to “wear” is that these verbs refer to the action of putting them on. Not the state of “having something on”, so when we want to say “I wear…”, we use ています instead.