one way would be to differentiate this 5 times and then put x=0.

the other method is:

[coefficient of x^0 in (1-x)^6]*[coefficient of x^5 in (2x+3)^4] + [coefficient of x^1 in (1-x)^6]*[coefficient of x^4 in (2x+3)^4]+...+[coefficient of x^5 in (1-x)^6]*[coefficient of x^0 in (2x+3)^4]

for this you can use binomial theorem.