At what level, though?
4E was weird because we found it was very easy to get through fights from like, level 1-7, but the nature of the abilities started changing after that, to way more Reactions, Interrupts, Immediate Actions, and so on, and by about 13, sudden we'd gone from easily getting a good fun fight down in 30-40 minutes to taking well over an hour, sometimes far over.
I haven't ever seen an actual, real, honest-to-god, at the table 5E group that can get through "several" i.e. at least 4 non-trivial fights in 1 hour. That's some unicorn stuff.
2? Maybe. Sometimes. 3? Never seen it done (usually we'd be looking more at 1hr 10 mins or more for that) but I could believe it, and I've seen close. More than that? Nah. I've never even seen that in a podcast or Twitch, even with less-RP-heavy groups, where they could get a fight done in full in 15 minutes, unless the fight was literally rated "Easy" by the CR calculation (or maybe "Normal" at the absolute outside).
The problem is it's a bit of false comparison even then. Because even "Normal" was "Easy" by 5E's CR calculations in DND Next, they just changed it last minute to being called "Normal" and added a super-easy even lower than that. So you'd really want to compare 5E Hard or very low Deadly to 4E Normal. And in that case, you're pushing it to get two 5E fights in an hour. You need decisive, engaged players who utterly ready for their turn and never have to look stuff up to make even theoretically possible. Ironically my experience is that 4E was much better at making players decisive and engaged, and the way it did abilities meant people usually didn't need to look them up.
So 5E is faster, and a LOT faster than higher-level 4E (and 5E doesn't slow down that much at higher levels, which is definitely nice and more like 2E than 3E or 4E in that regard, both of which became absolute slogs), but I'm not your example is quite convincing.