Is it possible to connect a MacBook Pro 2011 to the LG UltraFine 5K display using a Thunderbolt 3 to Thunderbolt 2 adapter? 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.
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