Shipping costs with tax specified

  1. Make sure that you have the correct Tax Class set up for Shipping in

    Store > Configuration > Sales > Tax > Tax Classes > Tax Class for Shipping
    

    21% VAT (in the Netherlands)

  2. Make sure you have set the right Calculation Settings for Shipping Prices in

    Store > 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 choose Excluding Tax

  3. From your Question I assume that you have already set Price Display Settings for Shipping Prices to Including and Excluding Tax

  4. Set the proper Shopping Cart Display Settings for Display Shipping Amount in

    Store > Configuration > Sales > Tax > Shopping Cart Display Settings > Display Shipping Amount
    

    For example choose Including Tax