Welcome to the forum.
Yes, K&N does make a filter for the 2005. Maggie at Race&Street has some of the best prices and customer service. Here's a link:
PT Cruiser Filter - K&N Drop-in Available for 2006-07 Also: Race and Street
If you want to spend some more money, click back on the site to "Performance" and check out the systems that replace the whole stock air filtering system from K&N and other suppliers.
Will it help in mileage and performance. Any improvement in air intake will help the N/A (Non-turbo) PT. Letting the engine breathe better can only have positive affects.