We report five new measurements of central black hole masses based on Space Telescope Imaging Spectrograph and Wide Field Planetary Camera 2 observations with the Hubble Space Telescope (HST) and on axisymmetric, three-integral, Schwarzschild orbit-library kinematic models. We selected a sample of galaxies within a narrow range in velocity dispersion that cover a range of galaxy parameters (including Hubble type and core/power-law surface density profile) where we expected to be able to resolve the galaxy's sphere of influence based on the predicted value of the black hole mass from the M-sigma relation. We find masses for the following galaxies: NGC3585, M(BH) = 3.4(-0.6)(+1.5) x 10(8) M(circle dot;) NGC 3607, M(BH) = 1.2(-0.4)(+0.4) x 10(8) M(circle dot); NGC 4026, M(BH) = 2.1(-0.4)(+0.7) x 10(8) M(circle dot); and NGC 5576, M(BH) = 1.8(-0.4)(+0.3) x 10(8) M(circle dot), all significantly excluding M(BH) = 0. For NGC 3945, M(BH) = 9(-21)(+17) x 10(6) M(circle dot), which is significantly below predictions from M-sigma and M-L relations and consistent with MBH = 0, though the presence of a double bar in this galaxy may present problems for our axisymmetric code.NASA/HST GO-5999, GO-6587, GO-6633, GO-7468, GO-9107NASA NAS 5-26555Astronom