Not a perl solution, but you could look at the cookie (if that's how the page limit is being enforced) and see if there's an obvious way to spoof it (if, for example, the cookie just reads "page_views_so_far=5"). Your browser is just sending something like:

GET / HTTP/1.0
Cookie: page_views_so_far=5
[download]

and then two newlines. That's all the cookie transaction is. Note: there are probably other headers, too, especially if it's HTTP 1.1 ... you can view all the headers your browser is sending here (all except whatever cookie(s), of course).

BCE
--Your punctuation skills are insufficient!