To solve the equation \((2x + 7)(x - 5)(5x + 1) = 0\), we need to find the values of \(x\) that make the equation true. This is a product of three factors, and for the product to be zero, at least one of the factors must be zero.

So, we set each factor equal to zero and solve for \(x\):

1. \(2x + 7 = 0\)
2. \(x - 5 = 0\)
3. \(5x + 1 = 0\)

Let's solve each equation separately:

1. \(2x + 7 = 0\)
\[
2x = -7
\]
\[
x = -\frac{7}{2}
\]

2. \(x - 5 = 0\)
\[
x = 5
\]

3. \(5x + 1 = 0\)
\[
5x = -1
\]
\[
x = -\frac{1}{5}
\]

Therefore, the solutions to the equation \((2x + 7)(x - 5)(5x + 1) = 0\) are:
\[
x = -\frac{7}{2}, \quad x = 5, \quad x = -\frac{1}{5}
\]