Function composition of function of several variables

You can do something like:

gcomp[n_Integer] := Composition @@ ConstantArray[g[#, -5, 1.2] &, n]

Which you can then use as:

gcomp[3][{0, 0}]

Or perhaps even better:

gcomp[n_Integer, c0_, b_] := Composition @@ ConstantArray[g[#, c0, b] &, n];
gcomp[3, -5, 1.2][{0, 0}]

n=3;
g[{x_, y_}, c0_, b_] := {x^2 + c0 - b*y, x};
Nest[Function[t, g[t, -5, 1.2]], {x0, y0}, n]