Is delaying the Dhuhr prayer until one or two o'clock and the Asr prayer until five or five-thirty—due to sleep, preoccupation, or for no reason—considered negligence and a sin, or is it within the realm of permissibility?

As for Dhuhr, there is no sin in delaying it as long as it is prayed before its time expires, even if doing so means missing the virtue of hastening and performing it early. As for 'Asr, there is no sin in praying it before the sky turns yellow, but praying it after the sky turns yellow is a sin, except for an excuse such as sleep or the like; because its optional time ends when the sky turns yellow.