I see no problem with the amount of time between the core sleep and your nap, Verbors.
If you have trouble waking up at 5am, you might experiment with the length of you core a little. Most people's sleep cycles average 90 minutes, so if they wake up at a 90-minute interval (4.5 hours or 6 hours), they wake up feeling more alert. My sleep cycles are slightly shorter; I feel great after 4.25 hours, but a complete zombie if I wake up after 4.5. When experimenting with the length of your core, adjust by 10-15 minutes at a time, and try each length for 4-7 days.
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