E53 2005 3.0 strut shock ?
 

I learned the struts support the shocks and my one strut is bad, should I replace both the shock and strut on both sides? Or just struts on both sides?

The strut and the shock are one part on the E53 (an most other cars these days) - you change them as a single part. See part #6 in this image..

https://static-cdn.imageservice.clou...64600-ebay.jpg

There are many other wear-items on the front suspension too. Are you referring to the upper shock mount (parts #7, #8 and #10)?