Just follow those steps, and go from there. The 5 minutes is for getting your grain up to 152 - doughing in/stirring and temp stabilization. If you remove the "5 minute rise" text, does that ease your mind? You are going to dough in, stir and do your best to get equal temps throughout the mash, as close to your chosen mash temp as possible anyway.
I suppose they add the 5 minutes because technically you are not resting at your 152. With the additional 5 minutes, without it, in the end it does not make a difference at 70 minutes.
BS does take heat loss of the cooler into account, but I don't think it is good at it (even when configuring your gear). I typically add a couple degrees to what BS says for strike temps, and that is with preheating the tun as well. But that is also my gear and processes. You can figure out your setup.
You really need to take good notes to help figure out your temps. After the basic info (i.e.strike temp, grain temp, pounds of grain), note your technique and process. Your strike temp may be spot on, but if it takes you a long time to dough in, you can lose extra heat with the lid open and all the stirring.
Coolers lose heat differently. You need to take temps at regular intervals to see how much heat you are losing. But remember opening the top will lose heat. I have a digital thermometer with flexible cables I can put in the tun, shut the lid and monitor the temps, works great.
If you lose more heat than you can handle, wrap the tun (blankets, towels,sweat clothes, real insulation...) to insulate it.
Take good notes, adjust accordingly.