Mid 2010: Resolution poor on 4K monitor?

What exact Graphic card does it have in it?

4. Can I connect to my 4K Ultra HD TV or 4K display via Thunderbolt?

4K Ultra HD TVs are supported over HDMI or with Thunderbolt to high-speed HDMI adapters. Thunderbolt 2 is required to use a 4K display. All Thunderbolt 2 models support 4K displays at 30Hz in Single Stream Transport mode. Some models support 4K displays at 60 Hz in Multi Stream Transport mode. See HT6008 for more information on using 4K displays. Specific 4K DisplayPort displays are supported on Thunderbolt with a mini DisplayPort to DisplayPort cable.

http://support.apple.com/en-us/HT204154

• Every Mac Pro 2010 has more than one Mini Displayport.

• your display has:

Inputs

HDMI

1.4 x 2

DISPLAY PORT

1.2*1

• The cable from Mini DisplayPort to (full size) DisplayPort costs about US$10. It has none of the wacky compromises surrounding HDMI.

>> I recommend you get a Mini DisplayPort to DisplayPort cable, ditch the troublesome HDMI, and live happily ever after.

Make sure both ends of the cable is fully inserted into it port.

Mini DisplayPort is difficult to seat properly. You must push until essentially ALL of the metal-end of the cable disappears inside the jack.

Some displays have DisplayPort OUTPUTs as well as inputs. Be certain you have chose the correct connections, and that the display is set to take input from that connection.

Some Displays require you to use on-screen display (on the display itself, not on the Mac) to enable advanced features like DisplayPort 1.2

2560 by 1600 is the (DVI) resolution of the old Apple Cinema 30" display. I have used that, and it works fine at its full resolution, no issues.

Worked?

I don't know how it's possible but I get full 4K resolution (albeit at 30hz) on my imac mid-2010 connected to my 40" Philips 4k Monitor (PHL BDM4065)

I'm amazed such an old video card can send that many pixels to a second montior. It also seems to blink less than it did when the my Retina iMac connected to it in dp 1.1. Sure at 30Hz it's not super fluid, but I'm impressed nonetheless.

I run the beta of Sierra 10.12, not sure if they did something to make that work, but yeah, definitely a huge surprise to see a 5750 Radeon drive a 4k monitor full res.

The resolution is poor because it sounds like you are running the 4K display in 1920x1080 mode.

1. To get 4K resolution you firstly need a video card for the classic Mac Pro that supports 4K, original cards for the classic Mac Pro are unlikely to be able to achieve this, therefore consider a Nvidia GTX 680 or higher
2. Secondly you need to upgrade your operating system to a minimum of Yosemite 10.10.5, older versions do not support 4K properly
3. Thirdly you need to use a Displayport to HDMI 2.0 adapter, like this - http://www.club-3d.com/index.php/products/reader.en/product/displayport-12-to-hd mi-20-uhd-active-adapter.html the Dual Link DVI to HDMI approach would only support either 1920x1080 at 60fps, or maybe 4K but only at 30fps this is because HDMI 1.2 which is undoubtedly what you are using is not able to do 4K at 60fps
4. Finally you might need to enable Hi-DPI mode as per - https://www.tekrevue.com/tip/hidpi-mode-os-x/ you should then hopefully be able to select a 'scaled' display resolution which should let you enlarge the text and menus but still benefit from the extra resolution

Note: The Dual-Link DVI adapter can only do a maximum resolution of 2560x1600 pixels which is less than the 4K resolution.

Note: The GTX 680 has a full-size Displayport connector and does not have a Mini Displayport connector. It is possible to get adapter cables to convert from one to the other but in this case it will be simpler to get the full-size Displayport version of the Club-3D adapter.