at about 5 meters distance between the listener positioned near one wall and the speakers by the opposing wall?
Then it will require much bigger speakers to get a satisfying listening experience, small near-field monitors really aren't the way to go for that application. I have my setup in a 5x5m room with a listening distance of about 3,5m, using a pair of KEF R5 and one Monolith 12" THX Ultra sub and I wouldn't want to go any smaller there.
One THX Ultra rated sub would suffice in your room as well, two smaller ones might be better in terms of room interaction, but in terms of output that should be the ballpark you are looking at, calculate 600-1000€ for that, depending on your locally available options.
For mains I'd go with tower speakers, you seem to have plenty of space. The bigger volume of the boxes will help with efficiency. I'd really like to hear the Arendal 1723 Tower THX speakers at some point, but you probably don't need something that massive. Maybe something like Polk R700, they were going for 1299€/pair on Black Friday, just look for deals you can get in your country, calculate maybe about 2000€ or so for good speakers.
And then you should get an AVR, I bought a Denon X-2700H, with reasonably efficient speakers something like that will suffice without external amps. Don't spend too little, you want reasonably good room correction (preferably MultEQ XT).
That would be 3000-4000€ for the setup.
If that is way too much you can look for used components ... or buy cheaper new components.
I'd still get tower speakers, the cheapest reasonable options start at around 300€ per pair (Heco Victa 702 318€/pair or something like that), a cheaper sub (Polk HTS12 or Saxx DS 12 for around 300€ or comparable) a cheaper AVR (needs to have room correction and HDMI Arc if you are using it for home cinema, difficult new for under 500€, maybe used). A setup like that would start at 1200€ (with a new AVR), makes a lot more sense than near-field monitors.