Three mechanically alloyed (MA) and spark plasma sintered (SPS) CoCrFeNiNbX (X = 5, 20, and 35 at.%) alloys with an addition of 5 at.% of SiC were investigated. The face-centered cubic (FCC) high-entropy solid solution, NbC carbides, and hexagonal Laves phase already developed during MA. In addition, the SPS compacting led to the formation of oxide particles in all alloys, and the Cr7C3 carbides in the Nb5 alloy. The fraction of the FCC solid solution decreased with increasing Nb concentration at the expense of the NbC carbide and the Laves phase. Long-term annealing at 800 °C led to the disappearance of the Cr7C3 carbide in the Nb5 alloy, and new oxides—Ni6Nb6O, Cr2O3, and CrNbO4—were formed. At laboratory temperature, the Nb5 alloy, containing only the FCC matrix and carbide particles, was relatively strong and very ductile. At a higher Nb content (Nb20 and Nb35), the alloys became brittle. After annealing for 100 h at 800 °C, the Nb5 alloy conserved its plasticity and the Nb20 and Nb35 alloys maintained or even increased their brittleness. When tested at 800 °C, the Nb5 and Nb20 alloys deformed almost identically (CYS ~450 MPa, UTS ~500 MPa, plasticity ~18%), whereas the Nb35 alloy was much stronger (CYS of 1695 MPa, UCS of 1817 MPa) and preserved comparable plasticity.