From the question it is given that,

$2x+7\ge 5x-14$

So, by transposing we get,

$5x-2x\le 14+7$

$3x\le 21$

$x\le 21/3$

$x\le 7$

As per the condition given in the question, x is a positive prime number.

Therefore, solution set $x=\{2,3,5.7\}$