The key to happiness with the Raspberry Pi seems to be to find a good quality USB cable. There are many out there that are absolute rubbish and the price tag is no guide to quality. If you have a decent multimeter, measure the 5v rail on the GPIO connector - make sure it's at least 4.8v and preferably higher. If the voltage dips too low, the RPi will display a little rainbow icon thingy in the top right corner of the display. It also records the low voltage "event" and I have a script somewhere to read this flag. They have a nasty tendency to corrupt the flash memory card if the power supply / cable is not good enough, so pay attention to this.
5.5v sounds a bit too high to me. IIRC, the genuine power supply outputs 5.1v to help overcome the voltage drop in the cable, but 5.5v is probably a bit much.
Current consumed will vary depending on how hard the CPU is running, the brand of flash card and what USB devices you have plugged in. I'd think 750mA is plenty for normal use. If you have a mechanical hard drive attached, it'll be much higher. I run mine with a cheap Plox brand power bank acting as a "UPS". I've also run it from a Xiaomi brand power bank successfully.
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