[rifter72]

Are 4th edition books compatible with 5th edition, for example the cyberware or rules for cyberlimbs in the Augmentation book?

[All4BigGuns]

*shakes the Magic 8-Ball*

"Signs point to No."

In all seriousness, I highly doubt it.

[Mäx]

Mostly no, some specifig thinks from differend books can be ported over(like some magic traditions), but in general the rules changed too much.
Also if one is willing to do the work any and all weapons can be ported over by giving them similar changes as the officially ported ones have(in other word eyeballing a damage boost and accuracy stat).

[Redwulfe]

Since the base mechanics are similar you could convert some things easily but I don't think many things would be plug and play.

Red

[Dracain]

With a lot of things I would say no.  However, traditions work identically, so they could be used, the same can be said of mentor spirits (though you would need to add an Adept bonus).  Matrix stuff seems incompatible for the most part, and combat is hugely different, but the weapons could probably be adapted with a little work. 

[Psikerlord]

4e rigger stuff?