First find $f(5x)$:

$f(5x) = 2(5x) - 1 = 10x - 1$

Then compute $g(f(5x)) = g(10x - 1)$:

$g(10x - 1) = 3(10x - 1)^2 - 7$

$= 3(100x^2 - 20x + 1) - 7$

$= 300x^2 - 60x + 3 - 7$

$= 300x^2 - 60x - 4$