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The plot of the campaigns in Heroes 5 is completely canonical.
The plot of the single-player scenarios (like "A Tear for Ossir," "The Last Flight of the Falcon") is also canonical, but it is presented as a subjective account from the main character of the scenario.
However, some of the creature descriptions in the original game, not including the expansions, are non-canonical (Rakshasas are not spirits, Minotaurs are not slaves, etc.). The same goes for the appearance of some creatures (Liches are not skeletons, Black Dragons have eyes on their wings, etc.). Gremlins, in general, seem to no longer exist (although I'm not entirely sure about that yet).