What is the difference between - 5 squared and - 5 parenthesis squared?

-5 is essentially - 1·5

Order of operations says to do exponents first, so without parentheses - 5², you would square first then multiply by - 1, leaving you with an answer of - 25.

However, parentheses comes before exponents in order of operations, so with parenthesis (-5) ² would be 25.