To solve for $h(-4)$ given the function $h(x) = 5x - 1$, substitute $x = -4$ into the equation.

$h(-4) = 5(-4) - 1 = -20 - 1 = -21$

Thus, $h(-4) = -21$.

Would you like more details, or do you have any further questions? Here are some related questions you might consider:

1. What is $h(0)$ for the same function $h(x) = 5x - 1$?
2. How would you determine the inverse of the function $h(x) = 5x - 1$?
3. What is the slope of the function $h(x) = 5x - 1$?
4. How does the graph of $h(x) = 5x - 1$ look, and where does it intersect the axes?
5. How would the function change if the equation were $h(x) = 5x + 3$?

Tip: Always check your calculations by substituting the solution back into the original function to ensure it satisfies the given equation.