Hi,
You might want to try:
Show[Plot3D[x^2 + y^2 + 3, {x, -5, 3}, {y, -5, 3}, AxesOrigin -> {0, 0, 0}, PlotRange -> {-1, 10},
AxesLabel -> {"x", "y", "z"}, ClippingStyle -> None],
Graphics3D[{Arrow[{{0, 0, 0}, {5, 0, 0}}], Arrow[{{0, 0, 0}, {0, 5, 0}}]}]]
Cheers,
Marco