Your 5" height limitation is tough.
One (obvious) option is to get the best soundbar you can afford.
Another option is the Cambridge Audio Minx speakers (you'd want the 11/21 series over the 10/20 series). There is a dedicated thread here in the forum. Three of them are less expensive than a higher end soundbar and I'm guessing they would sound better, or at least as good. (Their dynamics and imaging are unusually good for such small speakers in that price range - very desirable qualities for HT listening.)
For both options a very, very good subwoofer - esp. one with lots of detail/accuracy in it's mid and upper ranges - would be a must since you'll have a higher than average (120 vs 80) crossover.
An example would be the SVS SB12-NSD or PB12-NSD. The SB version is uncommonly small for it's output while the PB version is bigger and a bit louder, but both have superb detail and would work great with small LCR speakers. In that price range there are several ID brand subs that would work well ... those are just two that I'm familiar with.