Ok, shutdown... then what?
I have (sorry, had) more than one Synology server in different locations precisely for the purpose of having redundant backup and high availability. Everything offsite is now powered down. Onsite I've yanked the CAT6 until I sort the ports out.
There is a lot at stake for Synology as a company in terms of how quickly they a) communicate this to customers (I found out from El Reg, not Synology), and b) how fast they patch DSM 5 and 4.*. They will need to re-gain trust. Ideally an independent audit of their DSM software. But even simple measures like allowing users to easily change standard ports (and by "easily", I mean in the GUI) would be a help right now.
As I start thinking about how to improve my resilience, buying more Synology kit isn't exactly top of the list. If they'd put half the effort spend on the "pretty" new GUI for DSM5 into improving security then we probably wouldn't have this problem.
I have USB hard drive backups of most data. The rest are in Amazon Glacier. If I have to pull data out off Glacier because of this then Synology can expect to receive the bill.