Answer
$1\leq m \lt 6$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 5\leq m+4 \lt 10$
Subtract $4$ from each expression.
$\Rightarrow 5-4\leq m+4-4 \lt 10-4$
Simplify.
$\Rightarrow 1\leq m \lt 6$
Hence, the solution is $1\leq m \lt 6$.