First, we compute $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$.
We want to find the value of $n$ such that $5 \times 8 \times 2 \times n = 5040$.
Dividing both sides by $5 \times 8 \times 2$, we get $n = \frac{5040}{5 \times 8 \times 2}$.
Simplifying, we have $n = \frac{5040}{80}$.
Further simplifying, we have $n = 63$.
Therefore, the value of $n$ is $\boxed{63}$.
The answer is: 63
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
For what value of $n$ is $5 \times 8 \times 2 \times n = 7!$?

### Answer:
