To put it in your terms, at 160mph you will cover 5 miles in 1min 52seconds... It would be very difficult, if at all possible to go from 160 to 186 in that time frame. The closer you get the longer it takes. On a top speed loop it takes several laps to get to speed.
Furthermore, the road needs to be perfectly straight and perfectly flat at those speeds or car is off. That limits you to highways, and even on a highway it's tough to go 5 miles without at least some amount of bend. And no way you're not going to run into traffic covering that much ground that fast. Basically, you're full of shit.
Final nail in the coffin: the car is PCM limited to 186, if you had approached the top speed you would know this, not suggest it is anything but, and most certainly not without respecting how slow the acceleration ticks up at those speeds.