We are given that $f(x) = \frac{x}{5} + X$ and $g(x) = 4-x$.
We are also given that $f(g(a)) = 5$.
To find the value of $a$, we need to substitute $g(a)$ into $f(x)$ and set it equal to 5.
Substituting $g(a)$ into $f(x)$, we have:
$f(g(a)) = \frac{g(a)}{5} + X$
Since $g(x) = 4-x$, we can substitute $g(a)$ into the equation:
$f(g(a)) = \frac{4-a}{5} + X$
Setting this equal to 5, we have:
$\frac{4-a}{5} + X = 5$
Multiplying both sides of the equation by 5 to eliminate the fraction, we get:
$4-a + 5X = 25$
Subtracting 4 from both sides of the equation, we find:
$-a + 5X = 21$
Multiplying both sides of the equation by -1 to isolate $a$, we get:
$a = -21 + 5X$
Given that the value of $a$ is -6, we can substitute it into the equation:
$-6 = -21 + 5X$
Adding 21 to both sides of the equation, we find:
$15 = 5X$
Dividing both sides of the equation by 5, we get:
$X = 3$
The value of X is 3.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Suppose $f(x) = \frac{x}{5} + X and $g(x) = 4-x$. If $f(g(a)) = 5$, find $a$.
If we know the answer to the above question is -6, what is the value of unknown variable X?

### Answer:
