Transferring photos from iphone4s to iphone5s?

My partner has upgraded from an iPhone 4S to an iPhone 5s we want to transfer his photos and apps onto the new phone he doesn't have them backed up on iCloud or iTunes so need to do it using a PC? Could someone please give me simple step by step instructions on how to do this

No, you can't - you have to install iTunes on the PC to get the apps from the old phone or sign in the new phone using the same user ID on the Apple Store.
Photos have to be transferred to from the old phone to a PC using the usb cable and the Windows file handler or the photo application that comes up.