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Remainder questions are often solved by looking for patterns.
What you can do is check a few numbers you know like:
(5^1 + 2) / 4 => Remainder = 3
(5^2 + 2) / 4 => Remainder = 3
(5^3 + 2) / 4 => Remainder = 3
And you can see that it's going to work with 5^18 as well.
The reason is that the remainder of 5/4 is 1, so the remainder of
5^n where n is a positive integer will also be 1.
Add 2 to that remainder and get the total remainder of 3.