It can still be difficult to finance more than four properties conventionally, and as Dan states below. I encourage you to run your complete situation by a home finance professional that you trust.
When I am faced with scenarios like yours, I do my best to see if there's a way to cost-effectively consolidate the financing that already exists BEFORE working on the purchase of the new property. So many times, I find that by refinancing one or more of the existing properties and getting cash out, the client is then able to buy the new property "all cash," and also get better terms on all of the financing that will remain.
You would be surprised to know how often the solution is available with the resources that already exist, but that might not be considered.
If I can be of service, don't hesitate to get in touch.