Hi Dan,
I think most of us would see that as too low for through the night, especially if your monitoring system doesn't alarm to wake you should you go low whilst asleep. For a long time I aimed to have my HB1AC at around 5, but not until I got continuous monitoring that I realised how low I was going overnight to achieve this.
Whilst not having hospital support, my GP prefers that I run between 6 and 7 overnight and I'm happy with that. I notice that you are new to the site, and while not assuming that you are new to diabetes, if you are, you should also study the honeymoon effect, where your pancreas starts to kick in and out. Unfortunately, it doesn't recognise the amount of insulin you may have already taken and cause you to hypo.
Hope this helps, Peter