I did not tested this particular thing, but I’m quite sure there will be issue here.
I could power Rock4 with almost any my ac adapters including those for cellphones, most of them don’t work reliably with 5 series, especially with added m.2 cards. 5B is just bigger and will need much more energy than smaller models.
This is not recommended (and there is big warning to not do that) but some pi5 users were not aware of this and … nothing happened. Maybe they were just lucky or pi5 has some kind of protection (pi4 was never protected at gpio side). I would not try that on Rock 5B/+ for sure 
Those are almost same cards, same chip, almost same design. Cheap alternatives comes with no support and no warranty, most dont’t have ASPM support.
Describe first how much and what drives You need, 3.5 inch require 12V rail, 2.5 almost for sure need 5V only.
You can power sbc with dumb 12V, You can easily add step down converter for 5V. Pico PSU is such converter that is designed with 12V on input and atx power supply on other side. It’s big and complicated plug that You don’t need.
Take a look at this guy:
This takes 12V on input and produce sata 5+12V on other end. Inside there is step down converter for 5V, of course 12V is just wired into input. If You plan to use 2.5inch ssd, then whole 12V cabling is probably not needed. Then something like this can be used:

(not exactly from usb but from step down converter).
Also You can think about some kind of backplane, those usually cost few bucks and looks like this:
this one is for 2.5 inch sata/sas drives.
You will find the one that suits You, some have custom power plugs, some comes with molex or sata ports. Usually they come with mini sas connectors (You’ll need reverse cable), some with sata plugs.
Once You will get this idea, You will start looking for whole cages with drive trays
ie: this
Or the one with mini sas:
LSI 8i works here, You will need pcie port (yet again with 12V), but as a bonus You will get hardware RAID, all led indicators, support for SAS and much more power consumption (ASM1166 is 2-3W, LSI card is 12W).
so finally You need to revisit all that stuff. There is no compact, power efficient and super simple setup. If You plan 10G networking then check out my thread about Rock 5B with PLX pcie switch. If You plan to keep it as small as possible then just ASM1166 and step down converter.