Not in qt5, as far as I know, and as far as this says: http://qt-project.org/doc/qt-5/classes.html

Admittedly, I didn't try qt5 myself, mostly because of this, so I could be wrong. But I doubt it, since this is a recurrent topic all around the internet. QNetworkAccessManager can't substitute QFtp, and qt5 has no QFtp, officially.

Yes, I know I can install it from gitorius or whatever, but that's out of what I am willing to do for several reasons that are not so relevant for the topic at hand.