I noticed no responses for awhile, decided to wait to see if anyone had something to say, apparently not.
Hope ya don't take this the wrong way but your request seems more like a complex list of requirements, each simple enough by themselves, but when combined becomes a far more complex site. Asking for "something like this" as you put it might be a problem, i.e. I've not seen one script that does all this:
1) Pulls x images to create thumbnails from database or whatever source
2) Displays x in row, allow picking from 1-5 from x
3) Also display lightbox style image popup when selected/mouse over
4) Process those selected as voted, involves server side form processing and database updating
5) Limit voting to once per day by storing IP in said database
And you didn't even mention how the "most popular" images would be displayed, so any advice we offer would have to involve simple database structures so you could adapt scripts to accomplish that easily in the future. Not to mention if your platform even supports database, assuming it does (MySQL) since you would prefer Wordpress integration if possible.
It comes down to this...
The closest I could find happens to be a WordPress module, it's called NextGen (image gallery) and comes with a voting extension:
http://wordpress.org/extend/plugins/nextgen-gallery-voting/
You could use that as a starting point and hack the rest. Beyond that, if you get no other recommendations, consider coding it from scratch as well because it might be less work than modifying someone else's code by dealing with incompatibilities and requirements and a steep learning curve overall to learn a very strict API.
I am just letting you know don't expect a simple response or single recommendation for all the features you listed. If it happens that way, or you can get NextGen to work for you, awesome. Just keep the expectations real.
Hope you understand what I'm getting at, and hope this helps you! Honest.
-jim