To solve for \( m \) in the equation
\[ m + \frac{1}{4} = \frac{5}{8}, \]
we first need to isolate \( m \). We can do this by subtracting \( \frac{1}{4} \) from both sides of the equation:
\[ m = \frac{5}{8} - \frac{1}{4}. \]
Next, we need to express \( \frac{1}{4} \) with a common denominator of 8:
\[ \frac{1}{4} = \frac{2}{8}. \]
Now we can substitute this back into the equation:
\[ m = \frac{5}{8} - \frac{2}{8}. \]
Subtracting the fractions gives us:
\[ m = \frac{5 - 2}{8} = \frac{3}{8}. \]
Thus, the solution is:
\[ \boxed{\frac{3}{8}}. \]