How do I sync Iphone 5 to new MacBook Pro without deleting what's on iPhone?

Question

I just purchased a new MacBook Pro and I have an iPhone 5 that has been synced with my PC.  When I try and sync the iPhone with the new MacBook ti tells me that it will erase what is on the iPhone and replace it with what is on the MacBook.  I want to sync all that is on the iPhone with the MacBook and not delete what is on the iPhone.
How do I do that without loosing any music, emails, photos, calender appointments, etc.?
Thank you for the help in advance.

Answer 1

A device can only sync with one library at a time.  Ideally you transfer the library from the PC to the Mac so it is still syncing with the same library.
iTunes: How to move [or copy] your music [library] to a new computer [or another drive] - http://support.apple.com/kb/HT4527 - a somewhat bewildering and not always easily understandable set of options.
Quick answer if you use iTunes' default preferences settings:  Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive.  Open iTunes and immediately hold down the Option (alt) key (shift on Windows), then guide it to the new location of the iTunes Library.itl file in the moved iTunes folder.
For the record there's this reference for iTunes 11 but it really doesn't strike me as having the specifics you need. iTunes 11 for Mac: Move your library to another computer - http://support.apple.com/kb/PH12168 
Windows users see tip at: https://discussions.apple.com/message/18879381
If you put it in the default location of Macintosh HD > Users > *User Name* > Music  then you don't even need to start with the option key held down, iTunes will automatically look for it there.  (Make sure there isn't anything already in the iTunes folder there that you want to keep since you will be replacing it with the one you are moving.)
If you don't have the library anymore then it gets messy.  You will have to use third party software to transfer the phone contents to the Mac and rebuild your library there so its content matches that of the old library so you are syncin the content back to the phone.
Some of the information below has subsequently appeared in a document by turingtest2: Recovering your iTunes library from your iPod or iOS device - https://discussions.apple.com/docs/DOC-3991
Your i-device was not designed for unique storage of your media. It is not a backup device and media transfer was planned with you maintaining a master copy of your media on a computer which is itself properly backed up against loss. Syncing is one way, computer to device, updating the device content to the content on the computer, not updating or restoring content on a computer. The exception is iTunes Store purchases which can be transferred to a computer.
iTunes Store: Transferring purchases from your iOS device or iPod to a computer - http://support.apple.com/kb/HT1848 - only purchases from iTunes Store
For transferring other items from an i-device to a computer you will have to use third party commercial software. Examples (check the web for others; this is not an exhaustive listing, nor do I have any idea if they are any good):
- Expod (free) - http://www.headlightsoft.com/expod/ - Mac, universal for 104.+ (newer machines try de-Tune)
- deTune (free) - http://www.headlightsoft.com/detune/ - Mac, 10.5+
- Senuti - http://www.fadingred.com/senuti/
- Phoneview - http://www.ecamm.com/mac/phoneview/
- MusicRescue - http://www.kennettnet.co.uk/products/musicrescue/
- Sharepod (free) - http://download.cnet.com/SharePod/3000-2141_4-10794489.html?tag=mncol;2 - Windows
- Snowfox/iMedia - http://www.mac-videoconverter.com/imedia-transfer-mac.html - Mac & PC
- iexplorer (free) - http://www.macroplant.com/iexplorer/ - Mac&PC
- Yamipod (free) - http://www.yamipod.com/main/modules/downloads/ - PC, Linux, Mac [Still updated for use on newer devices? No edits to site since 2010.]
- 2010 Post by Zevoneer: iPod media recovery options - https://discussions.apple.com/message/11624224 - this is an older post and many of the links are also for old posts, so bear this in mind when reading them.
Syncing to a "New" Computer or replacing a "crashed" Hard Drive - https://discussions.apple.com/docs/DOC-3141 - dates from 2008 and some outdated information now.
Copying Content from your iPod to your Computer - The Definitive Guide - http://www.ilounge.com/index.php/articles/comments/copying-music-from-ipod-to-co mputer/ - Information about use in disk mode pertains only to older model iPods.
Get Your Music Off of Your iPod - http://howto.wired.com/wiki/Get_Your_Music_Off_of_Your_iPod - I am not sure but this may only work with some models and not newer Touch, iPhone, or iPad.
Additional information here https://discussions.apple.com/message/18324797