To solve the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \), we can start by eliminating the fractions by multiplying every term by 4:
\[ 4 \left( \frac{3m + 5}{4} \right) - 4 \left( \frac{3m}{4} \right) = -2 \cdot 4 \]
This simplifies to:
\[ 3m + 5 - 3m = -8 \]
Next, we can simplify the left side of the equation:
\[ 5 = -8 \]
This leads us to a contradiction (5 does not equal -8). This indicates that there is no solution to the equation.
In conclusion, the system is inconsistent, and there are no values of \( m \) that satisfy the equation \( \frac{3m + 5}{4} - \frac{3m}{4} = -2 \).