Hi,
Then I'm not sure what the problem is. I tried to reproduce the problem on my end and it worked fine.
One thing you could try is to turn off the user account activation in the Joomla user manager options page to see if you still have the same problem when there is no activation going on.
And what if you go through the Joomla user registration form instead of HikaShop's ?
Also, if you have a cart as a guest, and you manually login to an existing account, do you also have the problem ?
Also, I can see you're using a build of HikaShop 5 from the 17th of October. Since then, we've added several hot fixes (which will also be included in the next release of HikaShop to be coming out soon). So I would recommend downloading again the install package of the 5.0.0 on our website and installing it on yours in order to get all the latest patchs. That might help.