Do you want to transfer everything from your iPhone 4 to iPhone 5 ? If so, please follow the steps below;
We can backup the old iPhone 4 to your computer using iTunes and then restore that backup to your new iPhone 5.
Download and install latest iTunes on your computer from here --> http://www.apple.com/itunes/download/
After downloading iTunes, make sure you install it by opening the downloaded file and following onscreen instructions. After installing iTunes, open iTunes. Then on old iPhone, go to Settings > iCloud and turn off Find My iPhone option.
Then connect the old iPhone 4 to your computer. iTunes will recognize it. Then select your iPhone icon at the upper left, next to Music, Movies etc icons.
This will bring the Summary screen of iPhone. Now, click Backup Now button and make sure "To This Computer" is selected there. This will backup the entire iPhone to your computer. Then disconnect the old iPhone.
Then connect the iPhone 5 to your computer and open iTunes. Select your iPhone at top left.
Then this time click Restore Backup button and from the list of backups, select the backup of your old iPhone 4 from the drop down menu. Click Restore. This will restore everything from old iPhone 4 to new iPhone 5 (everything on your iPhone 5 will be replaced with contents of iPhone 5)
There is another method to restore the backup of iPhone 4 to iPhone 5 using iCloud. If you already setup the iPhone 5, then you need to erase it and you will get an option to Restore from iCloud backup, so you can choose the backup of iPhone 4.On the 5, go to Settings > General > Reset and tap Erase All Contents and Settings. This will erase the iPhone 5. Setup it after erasing and choose Restore from iCloud backup. Choose iPhone 4's backup and make sure you sign in with the Apple ID/iCloud ID you used on your old iPhone 4.
(Make sure there is backup of iPhone 4 on iCloud - Do it from Settings > iCloud > Backup > Backup Now)
Please let me know if that didn't work, so I will continue to help you