The 5000 limit applies only it you use apex or leveraging Salesforce API to send outbound emails
Note if you are using the Salesforce standard screens then these limits do not apply! However sending to 100000 portal users is not possible one by one using UI and you will need an API(Say you see using tools like Data loader to insert and trigger this notification). Hence these limits will apply!
I suggest you use full copy sandbox to test this limit!
Edit
If you use certain methods like setTargetId() in apex that uses ContactIds or LeadID or UserId, these limits do not apply.
However if your apex uses an email address then these limits do apply!
My suggestion if you are planning to send 100000 emails per day please use another tool that's meant for it! Like marketing cloud or AWS SES service or MailChimp and so on