To simplify the expression \((1 + 5a)(1 + 5a)\), you can use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step process:

\[
(1 + 5a)(1 + 5a)
\]

First, distribute each term in the first binomial to each term in the second binomial:

\[
= 1 \cdot 1 + 1 \cdot 5a + 5a \cdot 1 + 5a \cdot 5a
\]

Now, perform the multiplications:

\[
= 1 + 5a + 5a + 25a^2
\]

Combine the like terms (\(5a + 5a\)):

\[
= 1 + 10a + 25a^2
\]

So, the simplified form of \((1 + 5a)(1 + 5a)\) is:

\[
1 + 10a + 25a^2
\]