Equalities are handled by ContourPlot3D, with RegionFunction carving a subset defined by inequalities:
ContourPlot3D[
x^2 + y^2 + z^2 == 5, {x, -1, 3}, {y, -3, 3}, {z, -3, 3},
RegionFunction -> Function[{x, y, z}, y^2 + z^2 <= 3 && x >= 0]]
Pay attention to the double == instead of single =
