Has anyone successfully connected the 2014 MBP to the LG 5k display?
5K is 5120 x 2880 pixels. Your 2014 MBP is capable of 4096 by 2160 pixels at 24Hz MAX via HDMI according to Apple and MacTracker. Your MBP's Thunderbolt 2 port maxes out at 3840 by 2160 pixels at 60Hz.
So your model of MBP simply isn't up to the task of running an external 5K monitor. This shouldn't be too surprising; no 5K monitors were on the market when your MBP was being designed. Apple likely had no view towards needing to support such a high resolution external monitor.
By the way, this is going to be very confusing, but you need to understand it. Your LG 5K monitor has four ports on the back. **All four have USB-C connectors.** Only one of them is meant to be used to connect your monitor to your computer. That port is marked differently than the other three, and it is a "Thunderbolt 3" port, NOT a simple USB-C port. The other three ports are simple USB-C ports, but they are there to attach other USB-C peripherals to, NOT for attaching your monitor to your computer. Basically, your 5K monitor acts as a three port hub for USB-C devices (or other USB devices via an adapter).
Most of the folks that I hear from who can't get their high resolution monitor to work don't understand that a Thunderbolt 3 port, and a simple USB-C port, look identical, but that a Thunderbolt 3 port has a much higher specification and is meant to be an attachment interface for monitors, while a simple USB-C port generally is not. So, when attaching to a Thunderbolt 3 port, you need cables/adapters/hubs...whatever you are using, that support Thunderbolt 3, not simply USB-C. Or, in other words, a USB-C cable/adapter/hub won't work with a Thunderbolt 3 device unless it is specifically designed to do so. And it will say so right on the box and/or in the advertising. e.g. "Supports Thunderbolt 3".
