The investment is likely to be in infrastructure, energy, technology and property, Ali Shareef al Emadi, the country's finance minister, told the BBC.
"Currently the UK is our first investment destination and it is the largest investment destination for Qatari investors, both public and private," al Emadi told the BBC.
"We have more than £35bn to £40bn of investments already in the UK", he said.
Al Emadi told the Financial Times that "if you take a longer view on it, we have a lot of confidence in the UK economy and we think there’s some opportunity in the market".
"Brexit will be a plus and minus for us. For a short-term investor looking at the pound, my assets are worth less. But we don’t look at it like that. There will be some accounting adjustments," he told the Financial Times.
The £5bn is a standalone investment and unrelated to a £10bn investment announced in 2013, al Emadi said.
QIA is the largest shareholder in supermarket Sainsbury’s with a 22% stake, and was part of a consortium which acquired a 61% share in the UK National Grid’s gas distribution network in December 2016. It is also part of the consortium which owns Heathrow Airport.