How can i add videos to my iphone 5

Videos in your iTunes library are selected under the Movies or TV Shows tab for your iPhone sync preferences with iTunes and under which tab the video is located depends on if you have designated the video as a movie or tv show with the video detail in iTunes.

For videos captured by your iPhone or from another digital camera that were imported by your computer are selected under the Photos tab for your iPhone sync preferences with iTunes along with having Include Videos selected there.

How can I add them without switching on syncing? The new version of iTunes is annoying about that. No drag and drop that I can see.

you can drag and drop by dropping it on the right side bar, which slides in when you start dragging a movie.

The most easy way is to enable "Wifi Sync", then syncing is done automatically when both devices are on the same network. Just make sure your movie or TV Show folder is checked for syncing.