I don't understand the problem:
U saying u can send out 5000 mails an hour = 10 hours -50000 emails
20 hours/ 1 day = 100 000 emails
10 days = 1000 000 emails
good things take time....
In case you could send out 1million mails instantly, would your salesteam be able to process 10 000 orders the very same day?