How to download older version of an app from AppStore if you have older version of iOS?

I just got an iPhone 5 which has iOS 10. But some apps need iOS 11 or higher. I knew that these apps can be used on iOS 10 before, because of my friend. I found several solution if I downloaded the app before with my Apple account, I could download it to old iOS from purchased section on AppStore. But I couldn't find any solution if I didn't download the app before. How can I download an older version of an app in this situation?

Okay I done it with using this method:

1. I found a friend who has a newer iPhone which has a newer iOS version.
2. Go to AppStore on her phone and click avatar picture to go to profile.
3. Scroll all the way down and you will see the "logout" button. Click that.
4. Now, go to up of this page and you will see an input area that you can enter Apple ID and password. Login with using your Apple ID information.
5. After that, search the app you want to download and install the app. If your friend's iPhone already has the app you want to download, you have to delete it before, so you can download it with using your Apple ID.
6. Then you can logout from your friend's AppStore and you can search for the app on your older iPhone.

When you try to download, now it will ask that "this is not compatible app for that iOS version, do you want me to download the last compatible version of this app for this iOS version?". Confirm and voilà!

But I don't know why Apple push us to login from our friend's iPhone just for one time.