a(x-1)^3+b(x-1)^2+c(x-1)+d
=ax^3-3ax^2+3ax-a+bx^2-2bx+b+cx-c+d
=ax^3-(3a-b)x^2+(3a-2b+c)x+(-a+b-c+d)
a=5
3a-b=6 => b=9
3a-2b+c=0 =>c=3
-a+b-c+d=10 => b=9