Your teacher taught you the Addition (or Additive) Property of Inequalities. It's also in your textbook.
If a > b, then a + c > b + c
In your case a = x and b = 5 and c = 1
If x > 5, then x + 1 > 5 + 1
Lets try a few for x values greater than 5, say x = 6 and 12::
6 + 1 > 5 + 1
7 > 6 true
12 + 1 > 5 + 1
13 > 6 true