What did you use to test the speed?
The 670MB/s is unrealistic for a 3x2TB RAID5 array so it’s almost certainly cached (non-flushed) writes and so the number would vary widely depending on the amount of RAM that’s available for caching and the constraints on the data (such as that quota).
That 15MB/s is much slower than I’d expect on such an array though, you should still be able to get 100MB/s from your setup, assuming nothing else is reading or writing data at the same time.
dd if=/dev/zero of=blah.img bs=4M count=50 conv=fsync
This will write 200MB of data to your disk, making sure that everything is actually written onto the drive rather than just kept in memory. One caveat though is that this is only reliable if compression is disabled, if it’s enabled, then you should use a source other than /dev/zero as /dev/zero compresses as well as possible and so will get you a much higher transfer speed than your drive is actually capable of.