Old English slæpan "to be or fall asleep; be dormant or inactive" (class VII strong verb; past tense slep, past participle slæpen), from Proto-Germanic *slepan (cf. Old Saxon slapan, Old Frisian slepa, Middle Dutch slapen, Dutch slapen, Old High German slafen, German schlafen, Gothic slepan "to sleep"), from PIE root *sleb- "to be weak, sleep" (cf. Old Church Slavonic slabu "lax, weak," Lithuanian silpnas "weak"), which perhaps is connected to the root of slack (adj.). Sleep with "do the sex act with" is in Old English:
Related: Slept; sleeping. Sleep around first attested 1928.