Multiply.

To multiply the expressions \( (5w + 3t)(5w - 3t) \), we can use the difference of squares formula, which states that:

\[
(a + b)(a - b) = a^2 - b^2
\]

In this case, let:
- \( a = 5w \)
- \( b = 3t \)

Now we can apply the formula:

\[
(5w + 3t)(5w - 3t) = (5w)^2 - (3t)^2
\]

Now, calculate each squared term:

\[
(5w)^2 = 25w^2
\]
\[
(3t)^2 = 9t^2
\]

Putting it all together:

\[
(5w + 3t)(5w - 3t) = 25w^2 - 9t^2
\]

Thus, the simplified result is:

\[
\boxed{25w^2 - 9t^2}
\]