Discount for all registered users

Is it possible to configure Hikashop, so that when an user signup completely he/she will get 5% discount - and that coupon code will be send to their mail address via acymailing

Yes. You can do that with the Essential/Business edition of HikaShop and AcyMailing.
In AcyMailing, you need to create a campaign with a follow-up email where you add a hikashop coupon tag.
More information on such coupon tags:
www.acyba.com/en/support/documentation/1...plugin-hikashop.html
More information on campaigns:
www.acyba.com/en/support/documentation/1...ailing-campaign.html
You will also have to configure acymailing to add the new users automatically to the user list of the campaign you created.
More information on the list subscription on registration:
www.acyba.com/en/support/documentation/1...n-regacymailing.html