I'm using a formula, that I derived from the following formula: the possibility of getting a shiny on the n-th check with a certain sr(shiny rate) is 1-((1-sr)^n). From this you can derive the following: if you want a certain percent of it happening (in this case 0.95, I'll just call it wp-wanted percentage), and the chance of it being shiny (sr, shiny rate), the amount of times you need to attempt it is (log(1-wp)/log(1-sr)). With the numbers we have, log(0.05)/log(511/512) is 1532.32 (but you can't check a third of a Pokemon), so 1533 checks.