I have owned the previous model, the ONKYO HT-S5400, since May 2011, and still love it. I would not consider myself a qualified audiophile, but do think I have a better "ear" than most people of my acquaintance, as they seem to be wowed by my HTiB when they get to listen to it. Before that I had bought two 5.1 HTiBs, of the kind that included the DVD Player---first a SAMSUNG, and later a higher quality SONY---but found that they didn't deliver the goods, especially with music, so I made the jump to a better option once the SONY died on me. In my case, the 5400 has proven to be great, since I would not be willing to spend much more on separate components; it has plenty bells and whistles and CD or FLAC music sound really nice on it. Also, I see you are yet to discover just how awesome lossless Dolby TrueHD or DTS-HD MA sound in 7.1 from Blu-ray movies, and it is ready for it. In short, I recommend it.
I can't say how much more separate components will give you, though I admit others posting here are much more knowledgeable than me, but for the money and seeing you are in a similar position to what mine was, that would be my call. Besides, the recommended POLK and YAMAHA combo are 5.1, whereas the ONKYO 5500 you mention, as well as the 5400 I own, are 7.1. On that note, BTW, if rear space is a problem, you can have Front Height surrounds, and let me tell you, they more than make up for it---this is how I originally had my setup but then changed to rears once I got ceiling mounts, but honestly it sounds great either way.
unfortunately, the newer 5500 model has quite a few negative reviews on amazon... Oh, well... Good luck!