You can connect the GL-A1300 to 5GHz DFS channels in STA (Client) mode using LuCi, but I don't believe that it can also work as a 5GHz Master / Repeater if on a DFS Channel (you can still use the 2.4GHz radio in AP / Master mode).
You need to first turn off the 5Ghz WiFi AP via the normal UI menu, then login to LuCi (System->Advanced Settings) and stop / disable the "repeater" service ([LuCi]System->Startup)
Now, using the [LuCi]Network->Wireless menu, Scan on the 5GHz adaptor for the SSID you want to connect to. It should find APs on all Channels, including DFS ones. Connect in Client mode (selecting the wan Firewall profile), Save/Apply and you should be good to go. You may need to Reset the adaptor and / or Disable the 5Ghz Master (AP) Interface and change the Country code to your current location.
One possible gotcha is that after doing this the 5GHz radio may become unusable in Master (AP) mode - it's visible to clients but they can't get a DHCP lease (and with many "DHCP packet received on wlan1 which has no address" messages on the GL-A1300 log). Most likely cause is that the interface has been removed from the LAN Bridge - you can re-attach it via the LuCi Wireless menu using the Edit option for the 5GHz Master SSID, after which all should work normally.
Don't forget to re-enable / restart the Repeater service if you subsequently want to use as a Repeater on non-DFS Channels.
This doesn't (and shouldn't) enable the the router to act as an AP on DFS channels - it's not certified - but I don't see an issue with it as a STA / Client as the AP it's connecting to should handle the radar avoidance.