ClearAll["Global`*"]
ϕ[x_,y_]=-3 (x^2) y - ((3 x (y^2))/2)+((x^3)/2)+(y^3)-2 x -y;
ψ[x_,y_]=3 (y^2) x - ((3 y (x^2))/2)+((y^3)/2)-(x^3)+2 y +x;
vx[x_,y_]=-D[ϕ[x,y],x](* 6 x y + ((3 (y^2))/2)-((3(x^2))/2)+2 *) ;
vy[x_,y_]=-D[ϕ[x,y],y](* 3 x y - 3 (y^2)+3(x^2)+1 *);

plot1a=ContourPlot[ϕ[x,y],{x,0,5},{y,0,5},Contours->20,ColorFunction->"Rainbow"];
bright=Function[{c},Hue[((1-c)*0.75)]]; (* makes a new table of brighter colors *)
plot1b=ContourPlot[ϕ[x,y],{x,0,5},{y,0,5},Contours->20,ColorFunction->bright];
plot2=ContourPlot[ψ[x,y],{x,0,5},{y,0,5},Contours->20, ContourShading-> none];
plot3=VectorPlot[{vx[x,y],vy[x,y]},{x,0,5},{y,0,5},VectorColorFunction->None,VectorStyle->Black,VectorScaling->Automatic,VectorSizes->{0,1}];

Show[plot1a,plot2,plot3]
Show[plot1b,plot2,plot3]