If my due dates was may 28th . what was the date window i most likely conceived?

Just a guess!: It's vague and therefore can be risky to count backwards from a calculated date, unless it's just for curiosity. If may 28 was estimated from your last normal period (which should've been august 22?) then you likely conceived on or close to september 3...But if cycles aren't 28 days that's probably off, and there's no scientific way to calculate a window.

Last august.: Provided you are certain of your due date, naegele's rule of thumb suggests 8/21 as the first day of your last menstrual period (lmp), therefore you must have conceived ~2 weeks before that (i.e. 8/7). Of course, this rule hinges on the hypothesis that your cycle is regular and lasts 28 days. If that is not true, the estimate changes.