NHS England confirmed that all five people had been in the care of Shrewsbury & Telford Hospital NHS Trust (SaTH).
It means that the total number of people to have died with Covid at county NHS trusts has now reached 430.
Of the 430, a total of 400 have now died at SaTH, six at The Robert Jones and Agnes Hunt Orthopaedic Hospital near Oswestry, and 24 at Shropshire Community Health Trust.
Office for National Statistics (ONS) figures also show that 227 people have died in the county's care homes – 166 in Shropshire and 61 in Telford & Wrekin.
The ONS also says that 160 people have died with Covid in Powys.
Today's Shropshire figures come as NHS England said a further 973 people, who tested positive for the Coronavirus have died in the country, bringing the total number of confirmed reported deaths in hospitals in England to 68,894.
A spokesman said: "Patients were aged between 29 and 103 years old. All except 50 (aged 32 to 98 years old) had known underlying health conditions.
"Date of death ranges from 18 November to 26 January 2021 with the majority being on or after 21 January.
"Their families have been informed."