High Power LED strand Power Supply

If a module has only two terminals, but has some parallel LEDs internally, you can probably assume there's something inside the module to balance the current between each parallel circuit. This is made somewhat easier when all the LEDs are in one module because they can share a heatsink, and thus the temperature of each is likely close, and temperature variations are a big factor in why parallel LEDs will not share current equally. Each LED was also likely manufactured at the same time, so have very similar characteristics, which you can't guarantee when taking discrete LEDs out of a jar. The module may also include some small resistance in each parallel circuit to help balance. Point being: assume the manufacturer has taken care of this, and all you need to worry about is supplying the correct current to the two terminals provided by the module.

Your particular module is really like three modules, one for each color. It looks like there is one common terminal on the bottom, and three separate terminals on the top, one for each color. I can't find a datasheet that specifies if the cathodes or the anodes are common, so you may have to figure it out for yourself. It looks like maybe you can cut the common terminal apart if you want, but again, I see no datasheet, so you might have to experiment for yourself.

There is no special kind of LED driver that can drive parallel LED circuits. If an LED driver's job is to pump electrons, there's no way for it to tell some electrons to go down one circuit while telling others to go another way. The electrons decide which way to go by going whichever way minimizes their potential.

So, what you want to do with this module is power each of the R, G, and B sub-modules with a suitable driver (or if you can find it, one box that actually has three drivers in it). What you don't want to do is try to put the R, G, and B sub-modules in parallel and drive them all together. Since each color has a different forward voltage, this won't even remotely work: the color with the lowest forward voltage (red) will take very nearly all the current and all the power, and possibly be destroyed. At best you just won't get the other colors to light.

To try to get closure on this, and for my own sanity, I read Section 5.4 "Power Management" of the the BeagleBone Black System Reference Manual (BBB_SRM), Rev-C.1.

It says BBB uses two devices to supply the board with power:
TPS65217C has a Vin (Max) 5.8V
LDO TLV70233 has a Vin (Max) 5.5V
These are operating voltages.

The BBB_SRM says the "external LDOTLV70233 provides the 3.3V rail for the rest of the board."

However, searching the BeagleBone Black Schematic (BBB_SCH), Rev C, does not find the TLV70233.

There is a TL5209 on the "BeagleBone Black Power Management" schematic. It is connected to an output of the TPS65217C. It is not connected to the input power socket, and hence isn't directly constraining the maximum DC voltage input. It provides 'VDD_3V3B', so I believe it is the LDO referred to in section 5.4 of the BBB_SRM.

The text of section 5.4 is the same as the Rev-A6 BBB_SRM, so I suspect the text of the BBB_SRM is out of synch with the BBB_SCH Rev-C.

Summary @Farham is correct.
The only active part connected to the DC socket is the TPS65217C, and it has a maximum operating voltage of 5.8V. So 5.24V should be fine.

I assume the BeagleBone Black engineers specify The DC supply should be well regulated and 5V +/-.25V to provide some headroom; the BBB power management subsystem will survive voltages more than 10% over nominal.

Edit: I have raised an issue about the inconsistency of LDO part number of section 5.4 of the BBB_SRM and the "BeagleBone Black Power Management" schematic BBB_SCH at BeagleBone Black github