To solve the expression \( \frac{19}{25} - \frac{4}{25} \), you can subtract the numerators since the denominators are the same:
\[ \frac{19 - 4}{25} = \frac{15}{25} \]
Now, simplify \( \frac{15}{25} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{15 \div 5}{25 \div 5} = \frac{3}{5} \]
So, the simplified result is \( \frac{3}{5} \).