How do I stop my text messages and emails from showing on my 5yr old's iPad?
You can logout from iMessage and the Mail app (or don't even log in with your accounts to start with).
To turn messages and email off you can do the following:
iMessage: Settings > Messages > iMessage OFF.
Mail: Settings > Mail, contacts, calendars > the email account > off or delete account.
You can still use your Apple ID on that iPad for the store account.
If you just want to turn of notifications of mail and iMessage you can do that in the notification centre under settings.