Most 5/4 pieces I ever played, had some driving reason for that time signature, so the rhythm felt natural within the piece. Some emphasize the 1. Some emphasize the 5. Many emphasize the 1 and the 4 or the 1 and both 4-5, which could also be written as alternating 3/4,2/4 or alternating 3/2,2/2. But that gets messy.
If there's no natural rhythm within the piece based upon the time signature, then the time signature itself doesn't really matter at all. You could write the piece in 1,200/4 and it would make just as much sense.
Right, but in the more common times (3, 4, 6) the feel of the rhythm remains even if you get outside the musical cadence that drives it. Which is what frequently happens if you want to sprinkle any pizazz on the drums and not just keep time the whole way. Whatever limb I go out on in those time signatures, my internal time always has me grounded in where I am in the measure, which is important for sticking the landing when I want to play something extra and still fall back in with the band where I need to.
In 5/4, if I step outside shadowing whatever hook is driving the 5/4 feel, it's internal chaos unless I actively count through it, and even then it's dicey for me because under the best of circumstances I relied on feel far more than I was used to counting. This probably didn't matter as much when I was in band and played set parts to sheet music. Set parts meant no deviation and sheet music gave me one thing at a time to focus on with a conductor up front telling me exactly how long that particular note should last. In set drumming in band contexts.....I just really struggled with 5/4. A lot of guys do, so I'm not alone there, but it is something to see these guys who can genuinely feel it and just go nuts in 5 and never lose where they are.
Incidentally, that kind of thing is scattered all throughout Sting's first few solo albums. Lots of odd times sprinkled in there, and again, the ones in 7 I can feel without thinking about it. The ones in 5 have these little parts where the drummer does something seemingly simple, but if I tried it, I'm asking for trouble. Quite oddly, imo, there's a song on the Mercury Falling album that's in 9/8, but sort of phrased like alternating measures of 5/4 and 4/4. You'd think that as much trouble as I have with 5, the problem would compound when the time signature constantly switches. But for some reason, I found that one very easy to play along to and even embellish and solo over. No idea why. My tiny Cajun brain does what it does. OTOH, my first introduction to such a thing was a Toto song in 9/8 that I never could get. The song itself drives the 9/8 time, as you say, but it's so weird and disjointed that I just couldn't get it. The 4/4 and 7/8 parts.....no problem. But it starts and ends with that 9/8, and just....neaux.