The b=2,a=2/9,f(0)=8/9.
If b is not 2, f(f(x)) at least 2 roots.
f(f(x))=a(a(x-5)^2)(a(x-5)^2+2-b) or f(f(x))=a(a(x-5)^2+b-2))(a(x-5)^2).
5,5+SQUAT(b-2)/a or 5,5+SQUT(2-b) are roots. contradiction to only one root 5.
The b=2,a=2/9,f(0)=8/9.
If b is not 2, f(f(x)) at least 2 roots.
f(f(x))=a(a(x-5)^2)(a(x-5)^2+2-b) or f(f(x))=a(a(x-5)^2+b-2))(a(x-5)^2).
5,5+SQUAT(b-2)/a or 5,5+SQUT(2-b) are roots. contradiction to only one root 5.