Can our body adapt to periodic fluctuations in sleep?
In the same way that it takes time to fully adjust to jet lag (~ 1 timezone/day), it is unlikely that the body can adjust to alternating patterns of 3hr gaps on wake time on a daily basis [Ref. 1].  We simply have not evolved to jump timezones.  The most healthy thing to do is to have one time to get up each day (5am) so that your body is in sync.

[Ref. 1]: Review about circadian rhythms