To simplify the expression $(5x + 1)(x - 4)$, apply the distributive property (also known as FOIL for binomials):

$(5x + 1)(x - 4)$

Step-by-step solution:

1. First: Multiply the first terms of each binomial: $5x \cdot x = 5x^2$

2. Outer: Multiply the outer terms: $5x \cdot (-4) = -20x$

3. Inner: Multiply the inner terms: $1 \cdot x = x$

4. Last: Multiply the last terms: $1 \cdot (-4) = -4$

Now, combine all the terms: $5x^2 - 20x + x - 4$

Simplify by combining like terms: $5x^2 - 19x - 4$

So, the simplified form of $(5x + 1)(x - 4)$ is: $5x^2 - 19x - 4$

Would you like more details or have any questions?

Here are some related problems you can try:

1. $(3x + 2)(x + 5)$
2. $(2x - 1)(x - 3)$
3. $(6x + 3)(x + 4)$
4. $(4x - 2)(2x + 3)$
5. $(7x + 5)(x - 6)$

Tip: When simplifying binomial products, always remember to combine like terms at the end for a neater expression.