The Samsung t5 is a USB3 drive (not a thunderbolt drive).
But that's ok. It should work fine.
First thing you need to do will be to ERASE the t5 drive using disk utility.
You didn't tell us which version of the OS you're using.
For High Sierra and earlier, erase to "Mac OS extended with journaling enabled, GUID partition format".
For Mojave and later, erase to "APFS, GUID partition format".
Now it's ready to get "cloned over" from the internal drive.
The best way to do this is with CarbonCopyCloner (which will clone the recovery partition, too). CCC is FREE to download and use for 30 days, using it for this purpose will cost you nothing.
NOTE:
Pay attention to the CCC download page:
www.bombich.com
You want to download THE CORRECT VERSION for the version of the Mac OS that you're using.
Open CCC and accept all the defaults.
You'll see 3 "boxes" in the main window.
LEFT BOX -- this is for your source (the internal drive)
MIDDLE BOX -- this is for your target (the SSD)
RIGHT BOX -- scheduling, you can IGNORE this one.
Set it up and just "let it go". It will take a little while.
When done, quit CCC and open the startup disk preference pane.
Click the lock and enter your password.
Now select the external SSD as the new boot drive.
Close system preferences and reboot.
Do things go a little faster now? (they should).
Once you get logged in, go to "about this Mac" (Apple menu) and check to see that you are booted from the SSD.
That's really all there is to it.
TIP:
I recommend that you used the internal drive as your new "backup" to the external SSD.
You can use CCC at regular intervals to do an "incremental cloned update" to the internal drive, thus "keeping it the same as" the external boot SSD.
You ALWAYS want to maintain a SECOND bootable drive for emergencies.
ALWAYS. Even if it's the old and slower internal drive...