According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 11 words with the pattern --M-ST. That is, six letter words with 3rd letter M and 5th letter S and 6th letter T. In alphabetical order, they are:
almost
bemist
demast
demist
gamest
inmost
lamest
tamest
timist
upmost
utmost
Six letter words using the letters 'nuspiegn' are ensign, supine, and genius.
A six letter work is sicker.
LEGACY
tidies
fervor
Versus.
NETHER
onward
iambus
Accord is a six letter word. Accrue is another six letter word.
There are no English words that meet the criteria, even when you repeat the letters (which you need to do to make five letters spell a six-letter word).
alpaca