Answer
$\left[ -2,\infty \right)$
Work Step by Step
Solving the inequalities separately results to
\begin{array}{l}
-5x\le10\\
x\ge-2
,\\\\\text{OR}\\\\
3x-5\ge1\\
3x\ge6\\
x\ge2
.\end{array}
Using the conjuntion "or" the solution set is the combined solutions sets of both inequalities. Hence, the solution set is $
\left[ -2,\infty \right)
$.