can my iphone5 connect to my lexmark wifi printer

it's not on apple's list of airprint compatible printers...there may be a 3rd party app but i don't know about those.

http://support.apple.com/kb/HT4356?viewlocale=en_US&locale=en_US

The Lexmark Pro705 is not Airprint compatible but you can use any third party apps which will allow you to print to your non-airprint printer or you can use our LexPrint app. It will need a host computer which will act as a bridge for your printer and iOS device.

Just go to http://bit.ly/KY8eCI for more info.