  We demonstrate that the general D=3, N=5 Chern-Simons matter theory possesses
a full OSp(5|4) superconformal symmetry, and construct the corresponding
superconformal currents. The closure of the superconformal algebra is verified
in detail. We also show that the conserved OSp(6|4) superconformal currents in
the general N=6 theory can be obtained as special cases of the OSp(5|4)
currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4).
