To solve the equation 100 - 7(x - 5) = 58, we can follow these steps:

1. Distribute the -7 to the terms inside the parentheses:
100 - 7x + 35 = 58

2. Combine like terms:
135 - 7x = 58

3. Subtract 135 from both sides to isolate the variable term:
-7x = 58 - 135
-7x = -77

4. Divide both sides by -7 to solve for x:
x = -77 / -7
x = 11

Therefore, the solution to the equation is x = 11.