Headphone user here 
My last run ins with speakers are creative inspire 2.1 2400 and Sony mini hifi system from 1999 or so.
I would like to get some guidance regarding size/power for some bookshelf speakers (no space for floor standing ones) in a 4 by 5 meter room (13x16 foot or so) with a low 2.1 m (just under 7 feet) ceiling.
THey will be used for music, tv/movie watching. From equipment i have an external dac, headphone amp.
Thanks in advance
You’re in luck, the market is full of excellent options for bookshelf speakers. What you need to tell us is very important. 1) What’s your budget 2) What are you musical preferences tastes 3) How loud do you want to listen? 4) You don’t have space for Floor Standing speakers, do you have space for an amplifier?
Speaker design, build and quality has made so much headway in the last 20 years, you will be very satisfied with the handful of recommendation I’m sure you’ll get from the folks here.
Budget opens options.
I would like to keep it bellow 500-600 euros. Regarding musical preference I listen to almost everything, except hip-hop, rap and metal. The speakers should play reasonably loud, but not that loud that people from another floor would have to come down/leave the house. Because this room is a converted basement with windows i have about 17cm wide ledge around the entire room and some shelves 26-27 cm deep, so and amp sideways would fit.
This info will give a better picture for hifi guides to curate a good setup for ya.