Figures from NHS England confirmed four patients died in the care of Shrewsbury & Telford Hospital NHS Trust, while one died in the care of Shropshire Community Health Trust.
There have also been a further six Covid-related deaths in Powys.
It brings the death toll up to 393 at Shropshire's health trusts since the pandemic began.
In total there have been 364 deaths at SaTH, six at Robert Jones and Agnes Hunt Orthopaedic Hospital near Oswestry and 23 at the community health trust.
Office for National Statistics data shows 160 people are suspected to have died with the virus in Powys.
It comes as NHS England said a further 789 people who tested positive for Covid-19 have died, bringing the total number of confirmed reported deaths in hospitals in England to 64,111.
A spokesman said: "Patients were aged between 8 and 111 years old. All except twenty-eight (aged 25 to 97 years old) had known underlying health conditions.
"Date of death ranges from 20 October 2020 to 20 January 2021 with the majority being on or after 17 January.
"Their families have been informed."