phpapi-20090626+lfs is a "virtual package" which another package may "provide". In your case, this is an older virtual package which
php5-ffmpeg requires, and which the newer PHP package doesn't provide. The quickest solution just to get everything working, if the PHP upgrade broke it, would be to downgrade PHP.
For a solution using the new PHP, you will need an updated version of
php5-ffmpeg, if that's available. I believe this is a package from an external repository (like a PPA), because I don't see it in the normal distribution repositories. If it isn't available, you'll have to try to build it yourself. That might not be possible with the updated versions of
ffmpeg and PHP, though ...
Given the specifics of how old
php5-ffmpeg is (as detailed here), I would try to change your application to avoid the use of this library in the first place, as it locks you in to (at least) an old version of
In the mean time, the easiest solution, in my opinion, is to downgrade PHP (and
ffmpeg, if necessary) to the supported version.