Solve the factored quadradic equation (x - 5)( x + 3) = 0

To solve the factored quadratic equation \((x - 5)(x + 3) = 0\), you can use the zero product property which states that if a product of two factors equals zero, at least one of the factors must be zero.

Setting each factor to zero gives:

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

Solving these equations:

1. From \(x - 5 = 0\):
\[
x = 5
\]

2. From \(x + 3 = 0\):
\[
x = -3
\]

Now, we have the solutions: \(x = 5\) and \(x = -3\).

The smaller solution is \(x = -3\), and the larger solution is \(x = 5\).

So, the final answers are:
- The smaller solution is \(x = -3\).
- The larger solution is \(x = 5\).