Yes. You should be able to access it in the same way you access it on a computer.
You don't say what service you use to share the drive from the router, it could be Samba (Windows networking), NFS, or DLNA/uPnP. ?
There are lots of ways to access the drive on the Q5. You could use Kodi, Media Center, or many other file browser / media apps you might install from Play Store.
Using Media Center. From home screen go Media Center. You have a choice of LAN (Samba), NFS, UPNP. I think you're most most likely to be using Samba so go LAN - Autosearch. You should see your NAS and then be able to click through to the attached drive. NFS amd uPnP work similarly.