$RecursionLimit = 1665; (* anything less fails for k0 = 10 *)
a[k0_, x1_, x2_, x3_, x4_, x5_] := Module[{k, b },
k = k0;
b = (k--; a[k, b, x1, x2, x3, x4]) &;
If[k <= 0, x4[] + x5[], b[]]]
a[10, 1 &, -1 &, -1 &, 1 &, 0 &]