I'm having the same problem. Cleared data.cache, uninstalled and reinstalled latest app. Nada. When I try to start Facebbook the only error message is "Unfortunately, facebook has stopped". Seems to loop in that so if I don't hit "OK" right away, I have to tap it a large number of times...
Re: Nexus 5 Problems & Issues
Got mine today. Works fine except while it does connect to the network, I am unable to get any mobile data unless connected to wifi. Neither Google nor t-Mobile can figure out why, :(