Connecting an external monitor to a Mac Pro Early 2009

My 30 inch Apple Cinema display appears to be on the way out. At this point, I would love to get on to my computer to take some files off before I scrap the system. The hard drive was replaced a few years ago. It is my belief that this is a monitor issue based on how the screen looks and because it is so old.

I bought an Asus VP28UQG 28" Monitor 4K/UHD 3840x2160 1ms DP HDMI Adaptive Sync/FreeSync and I called Apple before I made a purchase for some guidance. The first person told me that I should have no issues with my older graphics card with a high performance monitor. He said it would still work, it just wouldn't be able to utilize the maximum quality of the monitor. As for connecting it, he told me to buy a DVI to HDMI cable. This did not work. The next person I spoke to at Apple sent me a link to adaptors and I chose a mini port to DVI cable since it was one of the options for my Early 2009 system. However, this also is not working. I did plug the monitor into my 2015 Mac Book Pro with an HDMI cable and it does work, so there must be something I am doing wrong, or some kind of limitations with how I am connection the monitor. Does anyone have any suggestions or know what I can do to get the new monitor working?

Graphics Card: ATI Radeon HD 4870 512MB

OS 10.11.6