MBP mid 2015 initial Time Machine backup to Samsung T5 blindingly slow
Initial Time Machine backups do take a long time compared to subsequent backups. How long the first backup takes will depend on a number of factors, some of which you've already covered in your question.

As for your exact situation, it is possible that you have a faulty T5, but it's not the most likely option.

I've used a few of these drives on various Macs and have found them to be very fast, but in all cases they're connected to a USB-C port (not a legacy USB 3 port).

The first things I'd do is test the T5 by transferring only a few large files (e.g. a few movie files so that you're transferring about 5GB or so of data). I would then repeat the test, but with the T5 connected to the other USB port of your MBP.

The above tests should result in one of the following results:


transfer speeds anywhere between 100 MBps to 200 MBps on both USB ports
transfer speeds anywhere between 100 MBps to 200 MBps, but only in one USB port
transfer speeds still at a very low level, regardless of port


If you're getting transfer speeds you're happy with from both ports, then you know that your lack of speed is nothing more than the initial Time Machine backup having to process/copy a lot of files.

If you're getting transfer speeds you're happy with from only one port, then you know you have a problem with one of your ports and you should use the other for your Time Machine backups.

If you're not getting good transfer speeds regardless of the port, then further troubleshooting is warranted to isolate whether it's an issue with your MBP or your T5.

Let me know how you go.