#### Answer

$m=-\dfrac{20}{7}$

#### Work Step by Step

Using $a(b+c)=ab+ac$ (or the Distributive Property) and combining like terms, the value of the variable that satisfies the given expression, $
2(5-m)=5(6+m)
,$ is
\begin{array}{l}\require{cancel}
10-2m=30+5m
\\\\
-2m-5m=30-10
\\\\
-7m=20
\\\\
m=\dfrac{20}{-7}
\\\\
m=-\dfrac{20}{7}
.\end{array}