I no longer have the Sprint Note 3, and unfortunately will not be actively maintaining this thread. If you would like me to add more, comment or PM me the ROM link. Thank you
Hello everyone! I've had some users ask me how to do this, so for those who may be in the same situation, here is a guide to get Android 5.0.1 on your Sprint Note 3 (SM-N900p), for users that are SIM-unlocked and are on a different carrier than Sprint. This has presented me a few problems before, as you cannot go past the MJ4 modem, without losing access to SIM-unlock. In my experiences, I could never get any 5.0+ ROMs to work on my Note 3, while still being able to use/recognize a SIM card from another carrier. I could not get this specific ROM to boot on NC5, so NH7 (possibly newer) bootloader is required. This guide is based solely my own experiences, and a few reported successful users as well. Your mileage may vary.
I will not take responsibility for any damage done to your device, do this at your own risk and free will.
Alright, shall we get started?
I know this is a tedious process, and there may be quicker ways of doing the same thing, but I've found this method most reliable. Hopefully this will help someone as much as figuring it out helped me

Please report your results
Credits: Give thanks to these folks, they well deserve
[email protected] for AICP android 5.1.1
@nambavuong for the beautiful ROM, thank you
@bigbiff for bringing TWRP to our device
@freeza for MJ4 flashable modem
@micmars for stock NH7 flashable firmware
Enjoy folks, cheers!