There is not a way to directly run expressions in the document template itself. However, there is a way to accomplish what you want. What you will need to do is to create a new 'pre-processing' entity that has all the fields you need, including a field for DOB + 5 days. In the microflow that generates the PDF, you will need to create a new preprocessing entity and run calculations to populate all the necessary values. This allows you to use the standard Mendix microflow addDays function to add the 5 days you need.
It will introduce an extra step to your microflow, but it will give you complete control and flexibility to build the PDF with all the data you need.
Hope this helps,