The List
There are 356 5 letter words with H as the last letter. The highest scoring is ZILCH at 19 points in Scrabble, though Words With Friends prefers QUICH at 21. 11 of them contain no vowel at all: CRWTH, CWTCH, GLYPH, LYMPH, LYNCH, MYRRH, among others.
AARGHABASHAHIGHAIRTHAITCHALEPHALMAHALMEHANIGHAPISHARISHARRAHAWASHAZOTHBAITHBANDHBATCHBEACHBEATHBEECHBEKAHBELAHBELCHBENCHBERTHBIACHBIMAHBIRCHBIRTHBLASHBLUSHBOKEHBOOTHBOTCHBOUGHBRACHBRASHBRITHBROCHBROGHBROTHBRUGHBRUSHBUMPHBUNCHBUNDHBURGHBUTCHCANEHCATCHCHETHCHICHCINCHCLACHCLASHCLOTHCOACHCONCHCOOCHCOUCHCOUGHCOUTHCRASHCRITHCRUSHCRWTHCUISHCULCHCURCHCUTCHCWTCHDADAHDAWAHDAYCHDEASHDEATHDELPHDEPTHDERTHDITCHDOETHDONAHDOSEHDOUGHDUNCHDUNSHDUTCHEARTHEPHAHEPOCHFAITHFAUGHFETCHFIFTHFILCHFILTHFINCHFIRTHFITCHFLASHFLESHFLOSHFLUSHFORTHFOUTHFOWTHFRESHFRITHFROSHFROTHFRUSHFURTHGALAHGANCHGARTHGERAHGIRSHGIRTHGLYPHGNASHGOETHGOUCHGRAPHGRITHGULCHGULPHGURSHHAITHHANCHHARSHHATCHHAUGHHEATHHEIGHHEUCHHEUGHHEWGHHILCHHITCHHOOCHHOOSHHORAHHOTCHHOUGHHUMPHHUNCHHUTCHILLTHKANEHKAUGHKEECHKENCHKETCHKHAPHKHETHKNISHKOTCHKUTCHLAICHLAIGHLAITHLANCHLARCHLATAHLATCHLAUCHLAUGHLEACHLEASHLEECHLEISHLETCHLEUCHLEUGHLINCHLOACHLOATHLOTAHLOUGHLUACHLUNCHLURCHLYMPHLYNCHMANEHMARAHMARCHMARSHMATCHMEATHMEITHMENSHMERCHMILCHMIRTHMISCHMITCHMONTHMOOCHMORPHMOUCHMOUTHMULCHMULSHMUNCHMUSTHMUTCHMYNAHMYRRHNATCHNAUCHNEATHNEIGHNIKAHNINTHNORTHNOTCHNUDZHNYMPHOBEAHOMLAHOMRAHOOMPHORACHPARCHPATCHPEACHPERCHPILCHPINCHPITCHPLASHPLESHPLUSHPOACHPOOCHPORCHPOTCHPOUCHPSYCHPUJAHPUNCHQUASHQUICHQUOTHQURSHRAJAHRALPHRANCHRATCHRAYAHREACHREECHRETCHREWTHROACHROTCHROUGHROUTHROWTHRUNCHSAITHSANGHSAUCHSAUGHSAWAHSCATHSELAHSHASHSHISHSHUSHSIETHSIRIHSIXTHSKOSHSLASHSLISHSLOSHSLOTHSLUSHSMASHSMITHSMUSHSNASHSNATHSNUSHSOKAHSOLAHSOOTHSOUGHSOUTHSOWTHSPOSHSTAPHSTASHSTICHSUBAHSULPHSUMPHSURAHSWASHSWATHSWISHSWITHSYLPHSYNCHSYNTHSYRAHTAISHTAVAHTEACHTEETHTENCHTENTHTEUCHTEUGHTHIGHTILTHTITCHTOOTHTORAHTORCHTOUCHTOUGHTRASHTROTHTRUTHTUATHUMMAHUMRAHUNETHVAUCHVETCHVOUCHWATCHWAUGHWEIGHWELCHWELSHWENCHWERSHWHICHWHISHWIDTHWINCHWITCHWOOSHWORTHWRATHWROTHYECCHYIRTHYOUTHYRNEHYUCCHZILCH