I am trying to figure out how to show a different image to visitors each time they land on our homepage:
1st visit = Image A
2nd visit = Image B
3rd visit = Image C
4th visit = Image D
5th visit = Image E
> 5 visits = Image F
You have to use Adobe Target for this purpose otherwise it will be a very custom requirement in which have to develop your own custom plugins to detect the and store number of visits for every user and server different image different visit.
There is hackish way of doing this, but it would not be like personalization.
// This is demo example with logic
As mentioned by Amit, you can achieve this by Adobe Target.
Another way you could achieve this is by using writing your logic with use of Adobe Analytic (Real time web Analytics, Link:- https://marketing.adobe.com/developer/documentation/analytics-reporting-1-4/real-time and http://randyzwitch.com/real-time-reporting-adobe-analytics-api/ ).
I hope this would help you.
Thanks and Regards