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Yes, an HDMI connection will support Dolby 5.1. It is designed to carry 8 channels of uncompressed audio. Any HDMI connection will support current Dolby/DTS solution. Newer HDMI specs allow for Dolby TruHD.
The newest rules governing HDMI cables and connections say that manufacturers must list out approved features of cables and equipment containing HDMI connections rather than quoting the hdmi spec (1.2, 1.3, etc). It would be worthwhile to consult the information on your specific equipment to ensure what it does/does not support, however, Dolby 5.1 has been a part of the HDMI specification from the beginning.