What value will make the equation 3m+54−3m4=−2

To solve the equation \( 3m + \frac{5}{4} - \frac{3m}{4} = -2 \), we'll first combine like terms.

1. Rewrite the equation:
\[
3m - \frac{3m}{4} + \frac{5}{4} = -2
\]

2. Combine \( 3m \) and \( -\frac{3m}{4} \):
\[
3m = \frac{12m}{4}
\]
Thus,
\[
3m - \frac{3m}{4} = \frac{12m}{4} - \frac{3m}{4} = \frac{12m - 3m}{4} = \frac{9m}{4}
\]

3. Now, substitute back into the equation:
\[
\frac{9m}{4} + \frac{5}{4} = -2
\]

4. Combine the fractions on the left side:
\[
\frac{9m + 5}{4} = -2
\]

5. To eliminate the fraction, multiply both sides by 4:
\[
9m + 5 = -8
\]

6. Solve for \( m \):
\[
9m = -8 - 5
\]
\[
9m = -13
\]
\[
m = -\frac{13}{9}
\]

Thus, the value for \( m \) that makes the equation true is
\[
\boxed{-\frac{13}{9}}.
\]