The lowest cost solution to send 5000 short messages a month.

This mainly depends on how you want to send these messages. If you don't send it regularly, I suggest you go to Jumeng.com's Blessing SMS Channel, where you can send SMS online for free, and the number is unlimited.

If you want to send these short messages in groups, you'd better find a professional short message sending company, such as Shan Zhi Times and Jingman Road. According to your quantity, the cheapest price should be 8 cents/piece.

I hope it helps you.