Readynas 2304 Hard drive Upgrade

Not directly.  From SSH, you should be able to first convert to RAID1:

mdadm --grow /dev/md127 --level=0 --raid-devices=2

That assumes your volume is the default MD127.  Once you have done that, you should be able to use the GUI to add the remaining drives back to form a RAID5.  It's probably best to re-boot before the expansion.  The OS may not like the fact that there is already data on the drives that are no longer part of the RAID, so you may have to format them in the NAS or remove them and zero them with a PC.

Of course, that RAID1 is going to be non-redundant, so having a backup before you start this is highly recommended.

If you check mdstat to see which drives are paired, you could remove one drive from each pair with power off and then power up degraded before issuing the GROW command and hold those two drives until the RAID1 re-sync completes.  That will give you another pair you can start from if that step fails.

Frankly, a factory default and data restore from backup might not take any longer.   But the other method should keep your data available through the whole process except the re-boot, though there will be some slowdown.