#### Answer

$(-\infty,2)\cup(3,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
2x+4\gt10 \text{ or } 3x-1\lt5
,$ solve each inequality separately. Since the conjunction "OR" is used, the solution set is the combined solution sets of both inequalities.
$\bf{\text{Solution Details:}}$
Using the properties of inequality to solve each inequality separately results to
\begin{array}{l}\require{cancel}
2x+4\gt10
\\\\
2x\gt10-4
\\\\
2x\gt6
\\\\
x\gt\dfrac{6}{2}
\\\\
x\gt3
\\\\\text{ or }\\\\
3x-1\lt5
\\\\
3x\lt5+1
\\\\
3x\lt6
\\\\
x\lt\dfrac{6}{3}
\\\\
x\lt2
.\end{array}
Since "OR" is used, then the solution set is the combined solution sets of both inequalities. Hence, the solution set is the interval $
(-\infty,2)\cup(3,\infty)
.$