Boots has said 4,000 jobs will go, while John Lewis is shutting down eight stores, putting 1,300 jobs at risk.
The moves come amid warnings that new economic support from Chancellor Rishi Sunak will not be enough to stop millions of workers losing their jobs.
Mr Sunak admitted that he would not be able to protect "every single job" as the UK enters a "severe recession".
Boots is consulting on plans to cut head office and store teams and shut 48 of its more than 600 Boots Opticians practices.
It has not yet said which outlets will close, but about 7% of its workforce will lose their jobs.
John Lewis said department stores in Birmingham and Watford will not reopen as the coronavirus lockdown eases. It also plans to shut down its At Home stores in Croydon, Newbury, Swindon and Tamworth and travel sites at Heathrow airport and London St Pancras.