To determine whether the sum of \( \sqrt{25} \) and \( \frac{1}{8} \) is rational or irrational, we first evaluate \( \sqrt{25} \).
\[ \sqrt{25} = 5 \]
Now, we can add this rational number to \( \frac{1}{8} \):
\[ 5 + \frac{1}{8} \]
To add these, we can convert \( 5 \) to a fraction with a common denominator:
\[ 5 = \frac{40}{8} \]
Now we can add:
\[ \frac{40}{8} + \frac{1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \]
Since both \( 5 \) and \( \frac{1}{8} \) are rational numbers, their sum \( \frac{41}{8} \) is also a rational number.
Thus, the answer is:
Rational, because both addends are rational.