First, we subtract 5 from both sides of the inequality to get $-4x>12$.
Then, we divide both sides of the inequality by $-4$, remembering to reverse the inequality sign because we are dividing by a negative number, to get $x<-3$.
The largest integer value of $x$ that satisfies this inequality is $x=\boxed{-4}$.
The answer is: -4
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the largest integer value of $x$ for which $5-4x>17$?

### Answer:
