TurboTax can accommodate a maximum of 20 Forms 1099-R. This is because 20 is the maximum number that the IRS e-file format allows.
This answer applies to 2017 TurboTax, not to later versions. It appears that 2018 TurboTax allows an unlimited number of Forms 1099-R to be entered, but it's unknown whether there is some number beyond which you must file by mail rather than e-filing.
TurboTax Deluxe can accommodate all 5 of your 1099-R forms.
Here's how to enter your 1099-R in TurboTax: