Etymology
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Words related to fifteen

*penkwe- 

Proto-Indo-European root meaning "five."

It forms all or part of: cinquain; cinque; cinquecento; cinquefoil; fifteen; fifth; fifty; fin (n.) "five-dollar bill;" finger; fist; five; foist; keno; parcheesi; penta-; pentacle; pentad; Pentateuch; Pentecost; pentagon; pentagram; pentameter; pentathlon; Pentothal; Pompeii; Punjab; punch (n.2) "type of mixed drink;" quinary; quincunx; quinella; quinque-; quinquennial; quint; quintain; quintet; quintile; quintessence; quintillion; quintuple.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit panca, Greek pente, Latin quinque, Old Church Slavonic pęti, Lithuanian penki, Old Welsh pimp, Old English fif, Dutch vijf, Old High German funf.

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-teen 
word-forming element making cardinal numbers from 13 to 19, meaning "ten more than," from Old English -tene, -tiene, from Proto-Germanic *tekhuniz (cognates: Old Saxon -tein, Dutch -tien, Old High German -zehan, German -zehn, Gothic -taihun), an inflected form of the root of ten; cognate with Latin -decim (source of Italian -dici, Spanish -ce, French -ze).
met (v.)
past tense and past participle of meet (v.). Old English long vowels tended to shorten before many consonant clusters. Hence meet/met (earlier mette), five/fifteen, house/husband, break/breakfast.
quinque- 

before vowels quinqu-, word-forming element from classical Latin meaning "five, consisting of or having five," from Latin quinque "five" (by assimilation from PIE root *penkwe- "five").

*dekm- 

Proto-Indo-European root meaning "ten."

It forms all or part of: cent; centenarian; centenary; centi-; centime; centurion; century; centennial; cinquecento; dean; deca-; decade; decagon; Decalogue; Decameron; decapod; decathlon; December; decennial; deci-; decile; decimal; decimate; decimation; decuple; decussate; denarius; denier (n.) "French coin;" dicker; dime; dinar; doyen; dozen; duodecimal; duodecimo; eighteen; fifteen; fourteen; hecatomb; hendeca-; hundred; icosahedron; nineteen; nonagenarian; octogenarian; Pentecost; percent; quattrocento; Septuagint; sexagenarian; seventeen; sixteen; ten; tenth; thirteen; thousand; tithe.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dasa, Avestan dasa, Armenian tasn, Greek deka, Latin decem (source of Spanish diez, French dix), Old Church Slavonic deseti, Lithuanian dešimt, Old Irish deich, Breton dek, Welsh deg, Albanian djetu, Old English ten, Old High German zehan, Gothic taihun "ten."

fifteenth (adj., n.)

"next in order after the fourteenth; an ordinal numeral; being one of fifteen equal parts into which a whole is regarded as divided;" late 14c., from fifteen + -th (1). By 15c. displacing forms derived from Old English fifteoða. Compare Old Frisian fiftuda, Dutch vijftiende, German fünfzehnte, Old Norse fimmtandi, Gothic fimftataihunda, with ordinal -d where English has -th. As a noun by late 14c.

quinzane (n.)

also quinzaine, "group of fifteen; period of fifteen days," 1855, in a historical context, from French quinzaine "the number fifteen; a fortnight" (12c.), from quinze "fifteen," from Latin quindecim (see fifteen). In older use, "the fourteenth day after a feast day" (the fifteenth day by inclusive reckoning), mid-15c. French quinze also was the English name of a popular 18th century card game in which the winner was the first to get 15 points or closest to it without going over.