To solve the equation
\[
\frac{3m + 5}{4} - \frac{3m}{4} = -2,
\]
we can first combine the fractions on the left side:
\[
\frac{3m + 5 - 3m}{4} = -2.
\]
This simplifies to:
\[
\frac{5}{4} = -2.
\]
Next, we eliminate the fraction by multiplying both sides by \(4\):
\[
5 = -8.
\]
This is not a true statement, which suggests the equation has no solution.
However, if we were looking for values of \(m\) more directly, we can rewrite the original equation without fractions by multiplying everything by \(4\):
\[
3m + 5 - 3m = -8.
\]
When simplified:
\[
5 = -8,
\]
which confirms that there is no value for \(m\) that can satisfy the equation. Thus, there is actually no solution.
If there is more context needed or if the equation was misstated, please provide that detail for further assistance.