Math has to be off.
At highway speeds at around 60 miles an hour you will go let’s say 30 miles in 30 minutes.
At 30mpg, that would be a gallon in 30 mins at cruising rpm of let’s say 2000, and 30% throttle.
So in 15 minutes you would burn half a gallon of gas at 30%, or ~$2.
Divide that by ten to get 3% idle and you get 20 cents for every 15 mins if not more.
All I know is on average I let my car run for about 5 mins on remote start and my mpg for the week drops from 24 to 20, or around 100 miles less per tank, or $15 a week in other terms.
$60 a month for remote start operation of 5 minutes.
My 2 cents.
Edit: my math isn’t any better. I got only about 1.25 cents a minute so even cheaper by my math then your 5c a minute.