I swear I am obsessing about somthing that's months away, but I just want it over with, and I need to do it right the first time (like all of us here!). So, I am eligible for ILR from five years after my leave to remain began, which was at the start of my first FLR (M) on 5 June, 2013. So my ILR eligibility begins 5 June, 2018.
Also, you can apply up to 28 days prior to eligibility (and up to as late as the date that my current FLR (M) expires in July of 2018). Correct so far, yes?
So if I do in-person for my ILR application in May, I could have it granted, and my visa in hand, before my five years has fully elapsed? Is that right?