Many thanks for the dimensions... and the photos really help too.
What follows is based on the following assumptions (correct me if anything I write here is incorrect):
1. This is a dual use space (entertainment and relaxation);
2. The primary role of your entertainment system is TV, movies etc., but you sometimes listen to music;
3. You're happy with the general layout of home furnishings but may be willing to make minor adjustments to accommodate speakers etc. provided this doesn't result in silly stuff like putting speakers in the middle of hallways or in front of a fire place.
4. You wish to avoid undue constraints when choosing or upgrading future speakers. So let's base all of our work on four ohm speakers (somewhat difficult to drive) with an actual sensitivity of 85 dB/W/m (slightly worse than average sensitivity).
With these assumptions in place, let's consider some basic measurements:
1. Front speaker distance from front wall: ~1 foot;
2. Front speaker distance to primary viewing/listening area: ~9 feet or 3 meters (Requires moving your sofa ~3 feet from the back wall and adjusting the side chair accordingly. This serves two audio and one functional purpose:
A. Audio: It gives adequate room for the placement of a rear set of speakers, which should be well behind the "3-9" line of the listener. It improves acoustics by moving the listener away from the rear wall (which is likely the main reflection point for the front speakers.)
B. Functional. Creates a pass through between the sofa and the opening to the kitchen.
3. Rear speaker distance to the primary viewing/listening area: ~4 feet or 1.3 meters (making allowance width of the back of the sofa).
With these dimensions in place, let's turn to sound pressure levels. THX reference levels are, IIRC, 85 dB (I'm conscious of the weighting factor but it's unnecessary for calculations). That's as loud a continuous sound pressure as one can listen to for 8 hours without suffering hearing damage. For the purposes of scaring your boxer (nice looking dog, btw), demos, or rocking out in the next room, let's say that you want a system capable of delivering 90 spl (which is much, much louder than 85 dB) at the viewing/listening level.
Turning to Crown Audio's handy calculator...
https://www.crownaudio.com/en/tools/calculators
Plugging in the various values, and assuming 3 dB overhead, you'd need to deliver at least 57W RMS to the front speakers and 11W to the rear speakers to get your 90 dB sound pressure level. This illustrates how little power is actually needed to achieve loud sounds from average speakers.
But wait, there's more...
The values offered by the Crown calculator are very conservative because they don't take into account that the listener will be subjected to (in your case) sound pressure from five speakers. So let's turn add up the dBs from those five speakers using another handy calculator:
https://www.noisemeters.ca/apps/db-calculator/
Adding five 90 dB sources equals 97 dB, which is a massive 12 dB higher than THX reference levels (85 dB) and 7 dB higher than your maximum target sound pressure (90 dB). Plus, the Crown calculator factored in a 3 dB overhead before arriving at its wattage levels. So, with about 3 x 60W and 2 x 30W plus one or two powered subs (which I didn't factor into the spl totals because they only operate from roughly 20-90 Hz or so),you'll be able to listen to the audio track of movies or music at more than adequate levels.
The key to all of this, however, is quality. Those wattages assume that your selected amp is capable of continuous and sustained delivery of 60/30W into four ohm loads without (and I stress without) clipping. But let's be even more conservative by saying that the requirement is for the wattages we calculated to be at 8 ohms... in case you choose a speaker with an 8 ohm nominal impedance.
For ease of set up and consistency, you may wish to select amplifiers that are capable of delivering 60W RMS at your speakers' impedance to all five channels (rear included). The advantage to this is that it allows you to choose between one or five amps from the same manufacturer. This increases the likelihood that all amps will respond with the same linearity as volume increases, making it easier for room correction software etc. to do its job correctly.
The amp you choose could be a five channel one with one or two LFE outputs, an AV controller with LFE outputs plus a three channel amp for the front and two channel amp for the rear) or any logical combination.
I haven't gone into seven channels or higher because, frankly, it would violate some of the assumptions previously listed. Going that route would require speakers on stands at mid points in your room (hallway and fireplace) and/or suspended from your sloping ceiling. I suspect this could create some domestic friction, so let's avoid making this a part of the plan.
Things would be much different in a large rectangular non dual-use space away from main entry doors... but it's important to work with the space you have. Your space isn't ideal but it isn't bad either. The sloping ceiling has some advantages wrt keeping ceiling reflections from affecting the seating area, scattering etc. The windows on the front walll are reflective, but heavy curtains and speaker placement can help resolve this. The downside is that going seven channels or higher may be too much for your space, but this helps you focus on making your five channels "count" in terms of sound quality as opposed to spatial effects.
