To solve the inequality \( 1 + 5m > -3m - 19 + 13m \), we first simplify the right-hand side.
Combine like terms on the right:
\[ -3m + 13m = 10m \]
This gives:
\[ 1 + 5m > 10m - 19 \]
Next, let's isolate \( m \). First, subtract \( 5m \) from both sides:
\[ 1 > 10m - 5m - 19 \]
This simplifies to:
\[ 1 > 5m - 19 \]
Now, add \( 19 \) to both sides to isolate the term with \( m \):
\[ 1 + 19 > 5m \]
This simplifies to:
\[ 20 > 5m \]
Now, divide both sides by \( 5 \):
\[ \frac{20}{5} > m \]
Which simplifies to:
\[ 4 > m \]
Or, written in a more standard form:
\[ m < 4 \]
Thus, the solution is:
\[ m < 4 \]