Shipping costs with tax specified
Make sure that you have the correct Tax Class set up for
Shipping
inStore > Configuration > Sales > Tax > Tax Classes > Tax Class for Shipping
21% VAT (in the Netherlands)
Make sure you have set the right Calculation Settings for
Shipping Prices
inStore > Configuration > Sales > Tax > Calculation Settings > Shipping Prices
If you have entered € 5,00 in the Admin Panel then choose
Including Tax
If you have entered € 4,13 in the Admin Panel then chooseExcluding Tax
From your Question I assume that you have already set Price Display Settings for Shipping Prices to
Including and Excluding Tax
Set the proper Shopping Cart Display Settings for
Display Shipping Amount
inStore > Configuration > Sales > Tax > Shopping Cart Display Settings > Display Shipping Amount
For example choose
Including Tax