Originally Posted by
passerby
If you're at all interested in X-Men stories written in the 21st century, there are two series that you absolutely must read. These not only re-defined the X-Men for years to come, introducing new characters as well as re-shaping the old characters, but also made it a pure joy to read:
1) New X-Men by Grant Morrison
Not just the first story arc "E is for Extinction" but all of his run, that ends in "Here Comes Tomorrow". I believe there is an omnibus edition, or in 7 TPBs.
2) Astonishing X-Men by Joss Whedon
This is a follow-up to Grant Morrison's run. Again, get the whole run, as all the pieces culminate in the final issue - Giant Size Astonishing X-Me #1 These are collected in 4 TPBs, IIRC.
The above two exceeded the 5-book limit you set for yourself, but they're worth it.