© 2020 American Physical Society. We report a B-mode power spectrum measurement from the cosmic microwave background (CMB) polarization anisotropy observations made using the SPTpol instrument on the South Pole Telescope. This work uses 500 deg2 of SPTpol data, a five-fold increase over the last SPTpol B-mode release. As a result, the bandpower uncertainties have been reduced by more than a factor of two, and the measurement extends to lower multipoles: 52< <2301. Data from both 95 and 150 GHz are used, allowing for three cross-spectra: 95 GHz × 95 GHz, 95 GHz × 150 GHz, and 150 GHz × 150 GHz. B-mode power is detected at very high significance; we find P(BB<0)=5.8×10-71, corresponding to a 18.1σ detection of power. With a prior on the galactic dust from Planck, WMAP and BICEP2/Keck observations, the SPTpol B-mode data can be used to set an upper limit on the tensor-to-scalar ratio, r<0.44 at 95% confidence (the expected 1σ constraint on r given the measurement uncertainties is 0.22). We find the measured B-mode power is consistent with the Planck best-fit ΛCDM model predictions. Scaling the predicted lensing B-mode power in this model by a factor Alens, the data prefer Alens=1.17±0.13. These data are currently the most precise measurements of B-mode power at >320.