Binary Recurrence Sequences
JavaScript (ES6), 51 44 bytes

(x,y,z,a,b)=&gt;g=n=&gt;n&lt;y?z[n]:a*g(n-x)+b*g(n-y)


Note that the function is partially curried, e.g. f(1,2,[1,1],1,1)(8) returns 34. It would cost 2 bytes to make the intermediate functions independent of each other (currently only the last generated function works correctly).

Edit: Saved 7 bytes thanks to @Mego pointing out that I'd overlooked that the the passed-in array always contains the first y elements of the result.