I’ll start in short by saying that you will be fine. If you want to understand how I can be so sure, then read on with my apologies for the length. 
I would estimate that if your cables are the same as the ones in your photo, that cable is typically 18AWG gauge. Check the markings on the wires to confirm.
If it is indeed 18AWG, you’ll be OK, as the rated DC current for 18AWG cable is around 14A, from memory. You haven’t specified which drives you have, so I will go with the typical peak of 2A for an active mechanical HDD such as a WD Red Pro. The higher amount of current will be drawn from the 12V line, as it is the one that deals with the mechanical components, which draw more power than the 5V logic circuitry itself.
That peak current wouldn’t last very long anyway, since it’ll be generally just for start-up and then things chill out when it’s just running. Still, I’m going to run with that anyway for the sake of being conservative in our calculations.
So, five drives, 2A consumption each, that’s 10A in a 14A wire.
Again, that does not mean you will draw 10A constantly after start-up. I estimate it would go to less than half that, based on the same Red Pro’s average power requirement going down to 8.4W when active (let’s round off to 9W). I have no specification data on how that power is divided between the 5V and 12V lines but I’ll estimate about 25% for the 5V logic and 75% for the mechanical.
In which case, that divides the 9W into 2.25W for the 5V logic and 6.75W for the mechanical.
That makes your total current draw a total of (2.25 / 5 * 5) = 2.25A for the 5V and (6.75 / 12 * 5) = 2.81A for the 12V.
At around 3A per wire, for a wire that is rated to handle 14A DC at typical home operating environments, you’re fine. 