To solve the equation \( 3m + \frac{5}{4} - \frac{3m}{4} = -2 \), we can start by combining like terms.
First, we can express \( 3m \) as a fraction with a denominator of 4:
\[
3m = \frac{12m}{4}
\]
Now, substitute this into the equation:
\[
\frac{12m}{4} + \frac{5}{4} - \frac{3m}{4} = -2
\]
Next, combine the terms on the left side:
\[
\frac{12m - 3m + 5}{4} = -2
\]
This simplifies to:
\[
\frac{9m + 5}{4} = -2
\]
Next, we eliminate the fraction by multiplying both sides by 4:
\[
9m + 5 = -8
\]
Now, isolate \( 9m \) by subtracting 5 from both sides:
\[
9m = -8 - 5
\]
\[
9m = -13
\]
Finally, divide by 9 to solve for \( m \):
\[
m = \frac{-13}{9}
\]
Thus, the value for \( m \) that makes the equation true is:
\[
m = \frac{-13}{9}
\]