Confirmed, this GRC T550-TTB is a drop-in replacement to the original Sharp cartridge. Many thanks for noticing PC-5000 listed on that box! The original tape just says "Sharp" on one side, then "Made in Japan" on the other side - no more specific numbers.
It's not really an "ink cartridge" - it doesn't contain ink like the more typical printers have. I think a sliver of ink is held to the ribbon (or the tape material itself), and it is thermally transferred to the plain paper (sort of like a "micro-brand", hot metal). They say it is a one-time use cartridge, but I'm curious if it could be rolled back and used again for a bit.
The "print contrast" (a dial within the printer itself) is all the way up, the tape is tight, but the print quality still isn't super. It is better than the original tape that had been sitting for 30 years. The paper is a little hard to feed, I have to "walk it in" a bit. And it's one sheet a time, I'm not sure if there was a plain-paper multi-sheet feed solution.
The above print is from a "built in demo" of the system. You have to remove the bubble cartridge from the top, and ALSO remove the "BASIC ROM" cartridge that is in a compartment at the bottom of the system. With "all ROMs removed" of the system, then during power up you press ENTER and the system presents a little demo mode with a sample text editor and spreadsheet, and this "graphic demo" - to go to either the LCD screen or option to "hardcopy" to the printer.
With the BASIC ROM cartridge inserted at the bottom, you have to "boot" to MS-DOS 2.0 first from a bubble cartridge. There is a note in the manual that on very-early versions of the PC-5000, yes it would boot straight to the BASIC ROM, so you could have the "boot up to BASIC" experience. But the note in the manual says that was basically in the early prototype only, the production released systems require a cartridge with MS-DOS present. The BASIC.COM on the "boot cartridge" is small since it is just invoking stuff on the BASIC ROM at the bottom of the system. If you have no need or interest in BASIC, that BASIC ROM cartridge can be replaced with another 64KB/128KB RAM upgrade bubble-memory module instead.
Glad I can find replacement print tape now, can experiment more with the printing.
Now to find a disk drive compatible with this Sharp. The 37-pin connector at the back is not like the IBM PC disk controller, so it needs some Sharp specific/proprietary disk drives that I haven't come across yet.