Hanukkah
Some five letter words ending in H are:batchbeachbelchbirchbirthblushbrashbrushbunchcatchcoachconchcouchcrashcrushdeathearthfetchfifthflashfleshflushforthfreshgnashhatchlatchlunchlurchmarshmatchmorphneathninthnorthpeachperchplushpoochporchreachsixthslushsoothsouthteachtenthtoothtruthyouth
Syrah
Vetch
Death?
HalveHasteHeaveHedgeHenceHingeHordeHorseHouse
astonish
scottish
Falluja -as in Falluja, Iraq
Some five letter words ending in H are:batchbeachbelchbirchbirthblushbrashbrushbunchcatchcoachconchcouchcrashcrushdeathearthfetchfifthflashfleshflushforthfreshgnashhatchlatchlunchlurchmarshmatchmorphneathninthnorthpeachperchplushpoochporchreachsixthslushsoothsouthteachtenthtoothtruthyouth
Pharaoh, 7 letters only.
Vanquish is an eight letter word. Vermouth is another word beginning with v and ending with h.
hash
Slashsmashgnashbrashcrashstash.
beach
One is through.
hue
hashish, hashish,