LG 43UD79-B 43" UHD 4K Monitor and 27" iMac 2015?

I'm looking for advice on connecting my iMac to an external display for use as a second monitor.

I have an iMac Retina 5K, 27-inch, Late 2015 Core i7.

Video is, I believe, AMD Radeon R9 M395X with 4 GB.

I have an LG 43UD79-B 43" Ultra HD 4K IPS Monitor (a 43-inch 4K beast) that I'd like to use as a second, external display. The LG has a native resolution of 3840x2160. When connected to my Dell PC (admittedly, and the only display) it looks awesome. I'd like to use it on my iMac as a secondary display, too.

What's the best was to connect this external display (to provide the highest resolution)?

I tried connecting the display to one of the iMac's Thunderbolt ports (using a Thunderbolt-to-DVI adapter, or a Thunderbolt-to-HDMI adapter), and the best I can get on the external display is "1080p".

The only options available in Displays preferences for the second display are:

- 1600x900

- 1080p

- 720p

Is there any way I can get the native 3840x2160 (4K) on the external LG display? If so, how?

Or is this all the video card can deliver?

Thanks for the help

iMac Retina 5K 27" late 2015, 4 GHz Intel Core i7. 32 GB RAM, AMD Radeon R9 M395X 4096 MB

macOS Sierra 10.12.4