Multiply the binomials:

To multiply the binomials \((5 + 2i)(5 - 2i)\), we can use the formula for the difference of squares, which states that \((a + b)(a - b) = a^2 - b^2\).

In this case, let:
- \(a = 5\)
- \(b = 2i\)

Using the difference of squares, we can find:

\[
(5 + 2i)(5 - 2i) = 5^2 - (2i)^2
\]

Calculating each term:

1. \(5^2 = 25\)
2. \((2i)^2 = 4i^2\)

Since \(i^2 = -1\), we have:

\[
4i^2 = 4(-1) = -4
\]

Now substituting this back into the expression:

\[
(5 + 2i)(5 - 2i) = 25 - (-4) = 25 + 4 = 29
\]

Thus, the result of multiplying the binomials \((5 + 2i)(5 - 2i)\) is:

\[
\boxed{29}
\]