Can I phone 5S be backed up from a selected version that is not the most recent

Do you mean backed up or restored? You can RESTORE a backup to your phone as long as the backup was made with the same version that you have on the phone or an earlier version. You cannot restore a backup made with a later version to a phone with an earlier version (e.g., you cannot restore a backup made with 8.3 to a device running 8.2).

When you backup your iPhone, you are backing up the current condition.

Do you mean restore?

You can restore an older backup to a newer iOS version but you cannot restore a newer backup to an older iOS version.

Just to be clear, the backup consists of your settings and data only and not the operation system (iOS).