I'm 99% sure the raid is software raid, so the assembling is not hard. Assuming that you have connected 4 disks to a Ubuntu system, the procedure is:
Open a terminal (command prompt)
First identify your data partitions:
You're looking for 4 partitions sdx
2, about 1TB in size each. (the size is given in kB). I'll assume they are sdb2, sdc2, sdd2 and sde2.
Now install the software raid manager (internet connection needed):
sudo apt-get update
sudo apt-get install mdadm
When you connected all 5 disks, it is possible that the array is automagically assembled and mounted. However, I don't think this is the case with 4 disks. So assemble the raid array:
sudo mdadm --assemble /dev/md0 /dev/sdb2 /dev/sdc2 /dev/sdd2 /dev/sde2 --run
Create a mountpoint and mount:
sudo mount /dev/md0 /tmp/mountpoint -o ro
Now you can use the GUI to copy your data from /tmp/mountpoint.