Limiting selection choices on a multi-choice field based on what has already been selected

You cannot actually limit which fields will appear in a multiple choice field.

But I think you can prevent duplicate rankings using four form rules.

I will explain this using syntax from legacy forms, but there's probably similar functionality on new style forms, but I guess I don't know that for sure. 

If ranking field 2 equals ranking field 1 then action is to change ranking field 2 to blank. 

The next form rule would be if multiple conditions are true 

Any of the following are true

Ranking field 3 equals ranking field 1

Ranking field 3 equals ranking field 2

Then action is to change ranking field three to blank. 

... and then you keep going with the rules for ranking field 4 not being equal to any of ranking fields 3 2 or 1. And then similarly ranking field five is not equal to any of ranking fields for 4 3 2 or 1.