I had no reason to choose r5c1 except that it looked promising i.e. it was a lucky guess

I checked Sudoku Susser - it did something completely different!

r1c8=1 => r1c2=2 => r2c1=7 => r2c8=2 => r1c8=7

Since this is a contradiction r1c8 <> 1 => r1c2=1 => solution

PS : Actually now I can't see where that came from - here's another one.

A nice loop = r1c5-2-r1c2-1-r4c2-8-r5c1-1-r5c5-5-r1c5-2

Allowing elimination of 2 from r1c8 and 5 from r4c5

Followed by an XY wing r1c2, r1c8, r2c1 = 12, 17, 27

Allowing elimination of 7 from r2c8 (or alternatively 2 from r2c1)

All roads lead to Rome!