displaymacbook prothunderboltusb
I'm currently using the MacBook Pro (13'', early 2011) which contains a Thunderbolt port. Unfortunately, the LG UltraFine 5K display uses a Thunderbolt 3 (USB-C) port.
That's why I'm currently thinking about connecting them via a Thunderbolt 3 to Thunderbolt 2 adapter.
I'm aware that there were quite a few questions concerning this topic on the Apple homepage. But the answers there weren't really confidable and accurate.
There are many types of DVI adapter, I could type a load of stuff or just point you at Wikipedia.
The key point is that there is no such thing as a DVI adapter. It's just a generic term that covers the overall outline of the cable end, but what you really have is either a DVI-I or DVI-D adapter, in either Single or Dual link capability. Or it may be a DVI-A. Or there are others...!
It's possible that your splitter cable must be of the dual link types, characterised by the longer horizontal bar pin, and your Thunderbolt adapter may or may not be. Shouldn't matter which type, either I (Integrated with analogue signal in the pins above/below the horizontal bar in addition to digital) or D (Digital only) as I imagine you are not subsequently adapting them down to DSUB further down the line, the only thing that matters is if they are both dual link.
So it looks like you need a Thunderbolt/MiniDisplayPort to DVI Dual link - the official apple one is the digital only one without the analogue pins (DVI-D Dual Link), and thus should work, if you are worrying that you do not have the same pinout (i.e. you have DVI-I Dual Link on your splitter, and it looks as though the analogue ones have nothing to connect to) then don't worry, it won't need them.
EDIT - Additional Info
After the comments, I have decided that you have a DMS-59 connector that looks like this:
So what you really need is a MiniDisplay > DMS-59 adapter, and my google-fu suggests that this is not looking like a possibility, I think you would be better served abandoning this cable, and looking for a total replacement, Mini Display Port > 2 x DVI (Single is fine, I or D if you have 2 ports). This may also be a pain to find, and you may end up needing a MDP/Thunderbolt to Dual Link DVI, followed by a Dual Link DVI > 2 X Single Link DVI splitter cable!
Thunderbolt and USB are quite different protocols, so you can't just use a cable -- it would need to have active electronics in it to convert between the protocols. And that means it would cost a lot more than a cheap commodity USB hub and so no one would buy it -- they'd just get a hub instead. If you're concerned about the power drain, get a powered USB hub.
Best Answer
No, your 2011 MacBook Pro supports a maximum resolution of 2560 x 1600 on an external display. So even if you get the cable situation sorted you will not be able to use the display on full 5K resolution.
Source: MacBook Pro (13-inch, Early 2011) - Technical Specifications