13', or in your case 13" is well under a semi. If they are coming the other way, you are safe.
My worry is increased windage. Not from the front. That is the same. It is the height carried all the way to the back & the extra side profile for wind to hit broadside.
A trailer is not much more than a box of air. What is worse, all of the heavy stuff is often on one side. What do you get with a full profile 5er? You get that much more cubic capacity to heat or cool. You get a bunch of cupboards way up high where you cannot reach them without moving a tall step stool around.
Looked at a few of the full profiles a couple years ago. What were the designers thinking?