ParametricPlot3D[{x,y,x^2+y^2-5},{y,-3,3},{x,-3,3},PlotStyle->Opacity[.8],ColorFunction->(If[#3>0,Yellow,Blue]&),Mesh->False,BoundaryStyle->{Black,Thickness[.01]}]

ParametricPlot3D[{x, y, x^2 + y^2 - 5}, {y, -3, 3}, {x, -3, 3},
 MeshShading -> {Directive[Opacity[.8], Blue],
   Directive[Opacity[.8], Yellow]}, Mesh -> {{0}},
 MeshFunctions -> {#3 &}, BoundaryStyle -> {Black, Thickness[.01]},
 Lighting -> "Neutral"]

ParametricPlot3D[{x, y, x^2 + y^2 - 5}, {y, -3, 3}, {x, -3, 3},
 PlotStyle -> Opacity[.8], Mesh -> None, BoundaryStyle -> {Black, Thickness[.01]},
 ColorFunction -> cf, ColorFunctionScaling -> False,
 Exclusions -> {x^2 + y^2 == 5}, ExclusionsStyle -> Blue]