Let's start with the given equation:
\[ \frac{3}{2}m + 5 = m + 15 \]
To eliminate the \( m \) terms on the left side, we subtract \( \frac{3}{2}m \) from both sides:
\[ \frac{3}{2}m + 5 - \frac{3}{2}m = m + 15 - \frac{3}{2}m \]
Simplifying the left side:
\[ 5 = m + 15 - \frac{3}{2}m \]
Now, let's combine the \( m \) terms on the right side. We rewrite \( m \) as \( \frac{2}{2}m \):
\[ 5 = \frac{2}{2}m + 15 - \frac{3}{2}m \]
Combine the \( m \) terms:
\[ 5 = \left(\frac{2}{2}m - \frac{3}{2}m\right) + 15 \]
This simplifies to:
\[ 5 = -\frac{1}{2}m + 15 \]
Now, we can isolate \( -\frac{1}{2}m \) by subtracting 15 from both sides:
\[ 5 - 15 = -\frac{1}{2}m \]
That gives us:
\[ -10 = -\frac{1}{2}m \]
Multiplying both sides by -2 to solve for \( m \):
\[ 20 = m \]
So the final value of \( m \) is:
\[ m = 20 \]