There are 255 5-letter words ending with H in the ENABLE dictionary — 3% of all 8,636 words at this length. At 4 points, H is worth more than most tiles without being awkward enough to hold back for — it is generally better placed than saved.
The list divides into 22 groups by first letter, the largest being the 31 words with s…h. Scanning the right group is faster than reading the whole list, which is why it is broken up below rather than run alphabetically.
If you know more than one letter, this page stops being the fast way to find it. Enter what you have in the unscrambler — the Contains, Starts with and Ends with filters combine, and setting both length fields to 5 narrows this list to the handful your letters actually allow.