I drove a car with the emergency brake on for about 5 miles. Will it bring huge damage?

 

welcome to the forum, no, there should be no damage. Just a note, if you live on level ground and not a hill, you do not have to set your parking brakes. An automatic has "P" lock, and a standard place in 1st gear keeps the car from moving. Now if you live on a grade or steep hill, yes turn your wheel into the curb and park or 1st gear and the emergency brake on.

 

^i agree with the above poster