Paris Geek made a
very good suggestion.
But it is an interesting question that got me thinking, so, I'll share with you some speculations (from which you'll see why Paris Geek's answer is great (and it is also great because it is short, unlike mine).
I'd expect that the battery usage would depend on 1) how various options are set up for your account(s) in Aquamail, 2) how many messages you get, and 3) what version of Android (including phone flavor) you have.
If you get tons of messages, and they are arriving frequently, let's say, every 5 seconds you have a message in one of those 5 folders/accounts, then you would not notice the difference on top of the already high usage: battery usage will be about the same.
If you receive only a few messages per day, then there
might be some difference, but if there is, I would expect it to be minuscule. In this case, the biggest difference (but it is probably still rather small) could be in the traffic: When you have 5 separate accounts, you need to support 5 separate "IDLE" connections. That requires 5-times more network packets required for that. When the amount of messages is small, this "heartbeat" would be a more significant portion of the overall traffic.
In principle, under certain combination of the Android configurations (and version) - with respect to how it handles the radio (Wi-Fi or mobile), low signal (Wi-Fi or mobile data), and possibly some random factors (of when the packets are sent by the server to support the conncetion open), this difference in the traffic might yield a difference in the battery life. But how significant that difference would be, - you can determine only experimentally.
This discussion is primarily with respect to IMAP push. I am much less familiar with EWS push, and in that case, I would assume that the difference would be smaller, if at all, especially if you set to sync by the number of days as opposed to the number of messages.
BTW, for the scheduled sync, 5 accounts with 1 folder vs a single account with those 5 folders (with the same folders and messages otherwise) would also consume more data (relative to the overall consumption) due to the overhead for the login each time. Again, the difference would be more significant (relative to the overall traffic) if you have very few messages arriving, and "messages to sync" is set to a low number.
One important parameter to keep in mind if you were to test this, especially when we are talking about the "scheduled" sync: You want to have
comparable (between the two cases) settings for the number of messages to sync (and probably also for the number of messages to cache). Note, that comparable may not mean "the same".
At the moment I am not 100% sure (I am sleepy, and my brain is lazy to dig deep in the neuron network called memory) if those settings in the account are for the entire account (divided among all the folders being synced), or per folder. If it is the former (which I believe is the case), then in your comparisons, it should be set to the 5-times higher number when you have one account with 5 folders, compared to the 5 separate accounts.
