Here is the list of all the English words containing letters 5 and 7 not containing letters E, L, R, S and T grouped by number of letters:
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Lots of Words is a word search engine to search words that match constraints (containing or not containing certain letters, starting or ending letters, and letter patterns).
You can use it for many word games: to create or to solve crosswords, arrowords (crosswords with arrows), word puzzles, to play Scrabble, Words With Friends, hangman, the longest word, and for creative writing: rhymes search for poetry, and words that satisfy constraints from the Ouvroir de Littérature Potentielle (OuLiPo: workshop of potential litterature) such as lipograms, pangrams, anagrams, univocalics, uniconsonantics etc.
Please note: the Wiktionary contains many more words - in particular proper nouns and inflected forms: plurals of nouns and past tense of verbs - than other English language dictionaries such as the Official Scrabble Players Dictionary (OSPD) from Merriam-Webster, the Official Tournament and Club Word List (OTCWL / OWL / TWL) from the National Scrabble Association, and the Collins Scrabble Words used in the UK (about 180,000 words each). LotsOfWords knows 480,000 words.