The SATA card only supports up to 5x drives physically, so no way to check if it can support up to 8x.
With all due respect, I hear what you are saying but I'm don't quite understand it.
As you pointed out, there is an installed HighPoint RocketRAID 2720SGL PCIe card. By all appearances it is a bone stock off the shelf card that should support 8 drives. Well there are some minor differences such as no retention bracket and 16 pins are parallel to the plane of the card rather then perpendicular but this is superficial.
There are two suggested testing methods.
The first would be to disassemble the TarraMaster D5 and remove the blue card from the HighPoint RocketRAID 2720SGL PCIe card. Then install the HighPoint RocketRAID 2720SGL PCIe card in a PC and use two mini-SAS SFF-8087 to 4 SATA cables connecting to a total of 8 hard drives (4 HDDs for each of the two breakout cables).
The second method would be to partially disassemble the TarraMaster D5 by removing the blackplane that supports only 5 drives and blue card installed in the HighPoint RocketRAID 2720SGL PCIe card. Then use two mini-SAS SFF-8087 to 4 SATA cables connected to a total of 8 Hard drives (4 HDDs for each of the two breakout cables).
Then Boot the system and see if all 8 drives are accessible.
Edit:
OK, I see now that in this case TarraMaster has basically just used the HighPoint RocketRAID software utility to setup and configure RAID arrays. While dated it is functional. So one "might" be able to start up the HighPoint "RAID Management Pro" interface and find the total supported drives there if it is correctly reported.
So for RAID Management version 2.6.20 (or thereabouts) on the home page you should see top tab options that read:
Global View, Physical, Logical, Setting, Event, SHI, Recover, Logout and Help
Under the "Physical" tab, the reported "Maximum Link Width" should be the maximum supported number of HDD's (I think). I suspect it will be 8 not 5.
Under the same "Physical" tab, the reported "Current Link Width" should be the current number of HDD's installed (I think).
I see that there are TarraMaster D4 and D8 models which likely differ internally by the number of physical SATA ports on the backplane and possibly the PSU. However, the D8 costs almost ~$2600 USD.