Let's denote the length of the shorter section as \( x \). According to the problem, the longer section is 5 inches longer than the shorter section, so its length can be expressed as \( x + 5 \).
We are also given the information that twice the length of the longer section is equal to three times the length of the shorter section. This can be written as an equation:
\[ 2(x + 5) = 3x \]
Now we can solve this equation for \( x \):
- Distribute on the left side:
\[ 2x + 10 = 3x \]
- Subtract \( 2x \) from both sides:
\[ 10 = x \]
Thus, the length of the shorter section is \( \boxed{10} \) inches.