Are there existing solutions to delete any files older than x days?
You can use AWS S3 Life cycle rules to expire the files and delete them. All you have to do is select the bucket, click on "Add lifecycle rules" button and configure it and AWS will take care of them for you.
You can refer the below blog post from Joe for step by step instructions. It's quite simple actually:
https://www.joe0.com/2017/05/24/amazon-s3-how-to-delete-files-older-than-x-days/
Hope it helps!