Slow Wi-Fi internet connection with Mac Mini
Virgin claim the Mini is not able to pick up 5g signal because of its specification. Is this true?


No, this is not true. Both the Late-2012 iMac and Late 2012 Mac Mini have the same specifications in terms of Wi-Fi.


  Do we have to buy a new computer to replace the Mini?


No. If it was me, I would share the internet connection from the iMac to the Mac Mini via an ethernet cable. This should be easy enough since they're on the same desk.

To do this:


Connect the iMac and Mac Mini via an ethernet cable
On the iMac:


go to System Preferences > Sharing
in the service pane on the left, highlight Internet Sharing
in the Share Your Connection From drop-down select Wi-Fi
in the To computers from list tick the Ethernet port
in the service pane on the left, tick the Internet Sharing checkbox

To ensure the Mac Mini is using this connection instead of the 2g one, you can either switch Wi-Fi off or choose to change the preference order of your connections in the Network preferences pane so that Ethernet is listed ahead of Wi-Fi.


Once you've set this up, you should have a fairly good connection on the Mac Mini. 

In terms of why the iMac is getting the 5g signal and the Mac Mini isn't, it could be as simple as the iMac causing some sort of obstruction (especially if the iMac is the one closer to the Wi-Fi router). 

However, I have found more often than not many devices will connect to a 2g network in preference to a 5g network. While 5g provides a faster connection, it isn't as robust as a 2g connection. So, if distance is an issue (not likely in your case) or if there are physical obstructions impacting the signal, a 2g network is often better.