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We present HST photometry of 17 Cepheids in open clusters and their mean parallaxes from Gaia EDR3. These parallaxes are more precise than those from individual Cepheids (G<8 mag) previously used to measure the Hubble constant because they are derived from an average of >300 stars per cluster. Cluster parallaxes also have smaller systematic uncertainty because their stars lie in the range (G>13 mag) where the Gaia parallax calibration is most comprehensive. Cepheid photometry employed in the period--luminosity relation was measured using the same instrument(WFC3) and filters(F555W,F814W,F160W) as extragalactic Cepheids in SNIa hosts. We find no evidence of residual parallax offset in this magnitude range, zp=-3+/-4 muas, consistent with Lindegren:2021b and most studies. The Cepheid luminosity (P=10d, solar-metallicity) in the HST near-infrared, Wesenheit system derived from the cluster sample is M_{H,1}^W=-5.902+/-0.025 and -5.890+/-0.018 mag with or without simultaneous determination of a parallax offset, respectively. These results are similar to measurements from field Cepheids, confirming the accuracy of the Gaia parallaxes over a broad range of magnitudes. The SH0ES distance ladder calibrated solely from this sample gives H_0=72.8+/-1.3 and H_0=73.2+/-1.1 km/s/Mpc with or without offset marginalization; combined with all anchors we find H_0=73.01+/-0.99 and 73.15+/-0.97, respectively, a 5% or 7% reduction in the uncertainty and a 5.3 sigma Hubble Tension relative to Planck+LambdaCDM. It appears increasingly difficult to reconcile two of the best measured cosmic scales, parallaxes from Gaia and the angular size of the acoustic scale of the CMB, using the simplest form of LambdaCDM to join the two.