PowerShot® S5 IS Digital Camera: can i retrive deleted photos...

Have you saved all these deleted photos on the inner memory card of this digital camera?
If you have, you can try my steps to see whether your deleted photos are recoverable:
Step1. Stop using this camera in case that any new file would rewrite your original photos.
Step2. Insert this camera to your computer and prepare to restore your photos.
Step3. Download a deleted photo recovery freeware to your computer and start to retrieve all your deleted photos back:
http://blog4mark.blogspot.com/2012/12/photo-recovery-after-delete.html
In fact, this freeware has ever successfully saved all the inaccessible data of my friend off from his camera. So, I believe it can also work successfully on your camera memory card, too.
Simply read more information of this freeware here:
http://www.freeware-fix.blogspot.com/2013/02/photo-recovery.html
Step4. Save and back up all the restored photos on a different memory card or drive in case of data recovery failure.
Note: Next time, you'd better back up all your important photos on different memory cards or drives in case of the similar data recovery problems.

If you are using a memory card, take no more pics until you've recovered the photos, take the card out of the camera. This is to reduce the chance of you overwriting some of your "lost" photos. There are many good freeware photo recovery software options that are available to help you recover your photos. This blog article reviews and outlines several of the better ones.