To have infinitely many solutions, we need the equation to be an identity, which means the left-hand side must simplify to the same expression as the right-hand side.
Starting with -5x + __ = -5x - 7, we can simplify the left-hand side by subtracting the -5x from both sides:
-5x + __ -(5x) = -5x - 7 - (-5x)
Simplify further, we get:
__ = -7
So the missing number is -7, and the equation is -5x - 7 = -5x - 7, which is an identity and has infinitely many solutions.