You can connect up to six of the following properly-configured displays to your Mac Pro (Late 2013).

Six Apple Thunderbolt Displays (27-inch), Apple LED Cinema Displays (27-inch), or third-party Mini DisplayPort displays.

Three 4K displays: two connected via Mini DisplayPort and one connected via HDMI.

One 4K Ultra HD TV or 4K display using HDMI and four Apple Thunderbolt Displays (27-inch), Apple LED Cinema Displays (27-inch), or third-party Mini DisplayPort displays.

Two HDMI (HD or 4K) devices: one connected via HDMI and one connected via Mini DisplayPort with an HDMI adapter.

Six DVI displays. This configuration requires an active DVI adapter.

See Using 4K displays and Ultra HD TVs with Mac computers for a list of 4k displays that work with your Mac Pro.

When connecting your displays, make sure you're using a supported configuration by connecting them to the HDMI and Thunderbolt ports on your Mac Pro. Attach displays to different Thunderbolt busses when possible (see the figure below). Don't attach more than two displays to any bus. This means that if you use the HDMI port, be sure to then only use one of the bottom two Thunderbolt ports (Bus 0).

When you start up your Mac Pro, one connected display initially illuminates. Any additional connected displays display an image after your Mac is finished starting up. If one or more displays don't display an image after startup is complete, make sure your displays and any display adapters are connected properly.

If you're using Windows on your Mac with Boot Camp, it has different specifications for connecting multiple displays.