My 5th (top) floor apartment is shaking; what might cause this?
Normal Vibrations in Buildings Have Identifiable Sources
I've encountered a vast range of vibrations in multi-dwelling buildings I have lived. Hear are the ones I can remember:

washing machine spin cycle (this happens often and, if it matches the resonance of the building can travel throughout multiple floors)
dishwasher valves and drain pump (not very strong, but once the sound filtered through floors and walls, the sound and feel was disconcerting)
nearby trains
nearby garbage trucks and other heavy vehicles
dancing at house parties
active construction work
elevators
earthquakes
explosion nearby

Note that all these sources are not the building structure itself, and are fairly easy to track down.  I can't remember encountering a source of vibration or shaking whose source I could not pinpoint with a small amount if work.
Find the Source or Move Out
The most likely explanation for the vibrations/shaking is that it is being caused by something in or near the building and not the building structure itself.  With a reasonable amount of effort by you, your neighbors and landlord, you should easily be able to pinpoint the source of the vibrations/shaking.
If you still cannot pinpoint the source after putting some earnest effort into finding the source, it may actually be the building structure itself.  This is not that far fetched if the building was not engineered (building inspectors usually defer to a professional engineer for structural issues).
If your only conclusion is that the vibration/shaking is originating from the building structure itself, then you should move out - it is a bad sign.  Even if the building doesn't collapse, you will have made the correct decision with the information you had at hand at the time.