I'd advise against this, but it depends on exactly what your requirements are.
BLE connections are low power because the radio can turn when there is no data to transfer. A "connection" implies that the receiver and transmitter are tightly synchronized, but this synchronization falls apart if you push the connection interval out to 5 minutes. Usually, connection intervals are in the tens or hundreds of milliseconds range.
Most types of connections aren't going to be maintained in the background - your app is competing with others for antenna time and energy from the battery.
Radio connections are unreliable. You can't expect every transmission to arrive at the receiver intact, so using the phone to log data is likely to be disappointing, unless either:
a. you don't care about the occasional missing sample, or
b. you buffer samples on the logging device and upload historic data in a batch
Lastly, advertising isn't a great way to log data with any temporal precision. The advertising device is usually something with a real time OS and nothing better to do, so it can send advertising packets at regular intervals. The scanning device, however, doesn't know when those advertising packets are being broadcast, so it will generally turn on its receiver at irregular intervals. Even if it were to keep its receiver on permanently, it doesn't know what channel to listen to (advertisements cycles through three different advertising channels). On top of that, you can't fit much data in a regular advertising packet.
Extended advertising in BLE 5 allows for more efficient advertising of larger packets, but I don't know how much support for extended advertising is built into iOS and the various phone models.
If I were trying to make a data logger, I'd log on the device and have an explicit, user-driven data download procedure from a foreground app.
If you're more interested in status than logging, advertising might be an option. If your data requirements are low, and timing isn't critical - e.g. if you're monitoring temperature every 10 minutes, you might be able to leverage iBeacon technology.
