The figures, from NHS England, show that all five patients died while in the care of Shrewsbury & Telford Hospital NHS Trust (SaTH).
It means that the total of Covid deaths at county NHS trusts has now reached 358.
Of these the figures show that 333 have come at SaTH, with 20 at Shropshire Community Health Trust, and five at the Robert Jones and Agnes Hunt Orthopaedic Hospital.
There have also been 200 Covid deaths in care homes in Shropshire and Telford & Wrekin.
Figures from the Office for National Statistics also show that the number of Covid deaths in Powys has increased by seven to 154.
NHS England today announced a further 884 deaths in hospitals in the country.
It means a total of 58,712 have now died in hospitals in England.
A spokesman for NHS England said: “A further 884 people, who tested positive for coronavirus (Covid-19) have died, bringing the total number of confirmed reported deaths in hospitals in England to 58,712.
“Patients were aged between 27 and 101 years old. All except 48 - aged 38 to 101 years old - had known underlying health conditions.
“Date of death ranges from December 4 to January 13.
“Their families have been informed.”