You can use this:
(defun org-export-as-pdf-and-open ()
(interactive)
(save-buffer)
(org-open-file (org-latex-export-to-pdf)))
(add-hook
'org-mode-hook
(lambda()
(define-key org-mode-map
(kbd "<f5>") 'org-export-as-pdf-and-open)))
UPD
This requires org-mode
8.0.0 and up. It's easily installed with list-packages
.