Where can I find my iPhone backups?

You can only find a backup from early May if you haven’t backed up the phone since then. If you follow these instructions→Restore your iOS device from a backup - Apple Support you will be given a choice of backups to restore. But note that restoring a backup restores everything; it puts the phone in the same state it was in at the time the backup was made.

When you back up your phone only the latest backup is kept. You cannot restore an older backup, unless it was made before the most recent update, or if you archived an older backup (which is supported only on Macs).

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Backups of what?

What are you using to backup?