From x:y=2:3 y:z=4:5, we get: x:y:z=8: 12: 15.

So x = 8a, y = 12a and z = 15a.

Substitute x = 8a, y = 12a and z = 15a into 4x-2y+3z=53 to get 32a-24a+45a=53, so a= 1.

Therefore, x = 8a = 8, y = 12 and z = 15.