#### Answer

$m\lt6$

#### Work Step by Step

Use the Distributive Property and the properties of inequality to solve the given inequality, $
2(m+5)-3m+1\gt5
.$
Using $a(b+c)=ab+ac$ or the Distributive Property, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
2m+10-3m+1\gt5
.\end{array}
Using the properties of inequality, the solution to the inequality above is
\begin{array}{l}\require{cancel}
2m-3m\gt5-10-1
\\\\
-m\gt-6
\\\\
\dfrac{-m}{-1}\lt\dfrac{-6}{-1}
\\\\
m\lt6
.\end{array}