To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can start by simplifying the left side.
First, we can combine the terms on the left side:
\[ \frac{3m + 5 - 3m}{4} = -2 \]
This simplifies to:
\[ \frac{5}{4} = -2 \]
Next, we will eliminate the fraction by multiplying both sides of the equation by 4:
\[ 5 = -2 \cdot 4 \]
This gives us:
\[ 5 = -8 \]
Since this statement is false, the original equation has no solution. Thus, there is no value of \( m \) that can satisfy the equation. So the answer is that there is no value for \( m \) (or we can write "no solution").