I can't give definite information on this subject, it is an explicit question which someone at Amazon can give relevant information on.
That said, I believe CloudFront policies may include multiple statements. Their schema is similar to IAM policies but I don't think it'll work exactly how you're expecting.
With IAM policies, you're able to attach multiple statements to one policy but they are OR'd across the statements:
Generally, each statement in a policy includes information about a single permission. If your policy includes multiple statements, a logical OR is applied across the statements at evaluation time. Similarly, if multiple policies are applicable to a request, a logical OR is applied across the policies at evaluation time... IAM Policy Documentation
In the documentation you linked to, the Statement
key's value is an array which you can include multiple statements in but they'll be OR'd across them. There is further information on how the policies are evaluated which will help in limiting access to the files you're working on.
Giving access to five random files will be a challenge which I do not believe is accomplishable with CloudFront access policies alone. The conditions available aren't designed with this use case in mind.
As Rodrigo M pointed out, using the AWS API from a script can accomplish what you're attempting to do. Unfortunately that is the only route I can imagine which will accomplish what you're attempting.
If you find a way to accomplish this task using only CloudFront policies (without other AWS services), I'll be quite interested in the solution. It'd be a creative policy and quite useful.