Let g(x) = ax + b. Then g(f(x)) would be a(2x-3) + b
a(2x-3) + b = 2ax -3a + b = 5-4x
The x coefficients must match up, and the constants must match up as well, so
2ax = -4x
a = -2
We can then plug it into 2ax - 3a + b
-4x +6 + b = 5-4x
6 + b = 5
b = -1
so g(x) = -2x-1
x=4
g(x)= -2(4) - 1 = -8 - 1 = -9