  We study spherically symmetric solutions of an $SO(5)$
Chern-Simons--Yang-Mills-Higgs system in $3+1$ dimensions. The Chern-Simons
densities are defined in terms of both Yang-Mills fields and a $5$-component
isomultiplet Higgs. The $SO(3)\times{SO(2)}$ solutions are analysed in a
systematic way, by employing numerical methods. These finite energy
configurations possess both electric and magnetic global charges, differing
radically, however, from Julia-Zee dyons. When two or more of these
Chern-Simons densities are present in the Lagrangian, solutions with vanishing
electric charge but nonvanishing electrostatic potential may exist.
