You have three ideas:
- There is a specific set of five days, expressed by your 'the 5 days'
- The five days are consecutive, expressed by 'in a row'
- Employee A is called for all of those days, expressed by 'Employee A has a shift planned for each of'—observe that 'every' may not be used here because unlike 'each' it is never used as a substantive, only as an adjective. You may say, as @CoolElf points out, 'every one of', or you may say as I do 'all of', but not 'every of'.
The awkwardness arises from your use of 'in a row'. You treat this as an adjectival phrase modifying 'the 5 days', and this is entirely proper. You've covered ideas 1 and 2.
However: there is a competing, and I should guess more common, use of '# Y in a row' as an adverbial phrase—'He went to church 5 Sundays in a row'. This use embraces both idea 2 and idea 3. If you say 'Employee A is called for 5 days in a row', 'each' or 'all' is redundant. But: this use does not accommodate idea 1 gracefully—its intension is consecutivity (idea 3) and comprehension (idea 2), and 'for the 5 days in a row' just isn't English idiom.
So you're presenting your reader with two competing parsings of 'in a row'. What you need to do is either replace 'in a row' as your lexicalization of idea 2 or eliminate the second parsing by displacing idea 1. Which you choose depends on where you want to put your focus. Your 'the' implies that the date in question has already been specified, so something like one of these:
- Employee A has a shift planned for all of these five consecutive days.
- Employee A has a shift planned for five days in a row at this time.