Old English finn "fin," from Proto-Germanic *finno (source also of Middle Low German vinne, Dutch vin), perhaps from Latin pinna "feather, wing" (see pin (n.)); or, less likely, from Latin spina "thorn, spine" (see spine).
U.S. underworld slang sense of "$5 bill" is 1925, from Yiddish finif "five," from German fünf (from PIE root *penkwe- "five") and thus unrelated. The same word had been used in England in 1868 to mean "five pound note" (earlier finnip, 1839).
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).