There was a game I almost played in rank until one of my teammate que dodge since he was scared of the enemy team's setup. I remember there was Ammumu, Galio, Missfortune, Fiddlesticks, and Xinzhoa in the enemy team. I was wondering, does this team setup dominate teamfights? And if they do, what's the best way to counter them?

This setup doesn't seem bad. Possible good jungler, tank, AP/AD carries. Nothing really shines about it though.
Edit: Good aoe synergy with the ults though.

Generally, DONT LET AMUMU ULT YOU.

The idea of that team is just that, to dominate teamfights. If they chain galio+mumu properly, fid/mf/xin wiill tear you apart. however, for any of that to work, galio and amumu has to ult your entire team.

qss will get you out of amumu or galio ults if you can time it right, but in either case it needs to happen before fid can show up.

Otherwise, being able to interrupt fiddle and mf will cancel a lot of their damage, but even still xin and mf can do a lot of damage.

Use Janna...?

i usually use AP blitz do deal with these things. either grab them out of the way, away from ur team, or grab them into your team so they can kill them quickly.

punch stops ults as well. things like kat's ult and nunu are the prime targets here. i dunno about galio. it might if u cast it right before he taunts u but before u can waste the punch on something else. the timing has to be perfect here.

ur ult also stops people from doing anything at all. that silence is HUGE for a teamfight. requires flash to really accomplish correctly but silencing the entire team is a huge deal.

the reason i say go AP blitz is for the burst. u need to be able to deal a large amt of dmg very quickly, and AP blitz deals a ton of dmg with his ult. u cant go and focus fire an aoe-ult team. they'll simply kill u before u can focus all of them down individually. u need to be able to do a significant amt of dmg in a short amt of time.

Besides Blitz, you have two options:

Stay slightly spread out. The only real danger there is the Galio/Amumu ults because they can trap you, keeping you in MF/Fiddle's ult. Their AoE's are really not that large. If your team stays slightly spread out, they will end up wasting their ults on a tank + 1 instead of your entire team. Of course, to do that, you need guys who can enter combat quickly once ults are popped. Janna, Ez, etc basically anyone with some speed and/or a flash. Also, tenacity, so you aren't stuck there forever if you are caught.

Or split push. This'll be a kite fest and/or tower sit while someone who can BD well safely (Yi, TF, etc) push another lane. This could be hard if their tanks get fed because Galio and Amumu will start diving pretty hard, making the 4v5 dangerous.

Janna

Jannnaaaaaa
Tristana and Alistar work nicely against fiddles and galio.
Alternatively you can skip the teamfight part and get a good split pushing team.