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571 five letter words begin with H, and more than half of them take A or O as the second letter.
A takes about thirty two percent and O twenty three, with E close behind at twenty. I and U pick up most of the rest.
HOTEL, HOUSE, HOURS, HUMAN and HEART are the most common entries, and they cover three different branches between them.
There is no HR, HL or HN opening in English. The second box is a vowel in nearly every entry, with Y the only real exception.
That makes the page unusually predictable in shape, even though the leading branches are close enough that none of them is an obvious opener.
HEART is the strongest single guess. It covers the E branch and its remaining four letters are among the most common in the language.
H is a breath sound rather than a hard consonant, so it needs a vowel immediately after it to be pronounceable at the start of a word.
HOUSE. Its S is far more common as an ending than the L in HOTEL, so a partial hit leaves you more to work with.
A small set including HYMNS and HYPER, where the Y is doing the work of a vowel. It is the branch to try once the five real vowels have failed.