Senior Kangaroo 2022 Q12

Five cards have the numbers $101$, $102$, $103$, $104$ and $105$ on their fronts.

$101$ $102$ $103$ $104$ $105$

On the reverse, each card has one of five different positive integers: $a$, $b$, $c$, $d$ and $e$ respectively. We know that $a+2 = b-2 = 2c = d^2 = e^2$.

Gina picks up the card which has the largest integer on its reverse. What number is on the front of Gina's card?