How old is your lo? Mine is 4.5mths (also on 4hr easy) and she also stirs/wakes around 5-ish. I usually reswaddle and give her the paci, then she usually settles until wake up around half 6-7am. On rare occasions, she'll just refuse to go back to sleep so I just start the day at 6am (then nap at 8am) and go on the 4hr easy from there. Sometimes, I do stretch her awake times and feed times by 15mins so that I can put her down by 6.30-7pm for the night.
Have you tried the paci instead of feeding at 5am? What you can do if she's not hungry is just pick her up and put her down again and see if she settles to sleep again til wake up time (I don't necessarily mean the pu/pd method). Otherwise, even if you do start the day at 6am, I reckon that extra hr should be ok for her because she's not doing any full on activity... If you feed her at 5am and she goes back to sleep, then usual wake up would be 7-7.30am and you feed her. Eventually, she'll just refuse the 5am feed completely and learn to sleep til the wake up time. This is what happened w/ my lo...
Hope this helps!