You don't have to carry the printout of your visa all the time for 5 years, just your passport with the permission to stay (arrival stamp or extension stamp, as the case may be).
Keep a copy of the eVisa document (PDF file) safely on your computer, your phone, in several places in the cloud. You will need to show a printout of it at the immigration desk every time you arrive in Thailand and give a copy to your local immigration office if and when you apply for the optional 180-day extension of stay.