Hi cmpinggrl,
I understand you have an Envy 5530 that is jamming all the time despite being new. I'm sorry to hear this, but I will certainly do my best to assist you!
I would suggest, since you've done all of the standard troubleshooting, that you start with plugging the printer directly to a wall outlet. This ensures it is getting all the power it needs to function properly.
If that doesn't resolve it, I would next recommend Getting the Latest Firmware and Product Updates on the front panel of your printer. I realize it's new to you but this update may have been released while the printer was still in the store.
If this still doesn't change anything, I'd suggest calling HP Tech Support and inquiring what they can do for you from this point.
Hope this helps, have a great day!!