Is it at all possible to have two different DSE versions in the same cluster? In my case, I have a a cluster of two DSE 5 nodes and another one of two DSE 4.8.9 nodes. Can I connect them such that data is replicated from DSE 4.8.9 to DSE 5 in real time?
No. If you were to try this, you'd be in an "Upgrade State." And clusters in an upgrade state are bound by these restrictions:
Trying something like this would be further exacerbated by the fact that 4.8.9 is based on Cassandra 2.1 and 5.0 is based on Cassandra 3.0. There were some significant changes between the two, so you would undoubtedly run into problems.
The best way to go about this would be to upgrade your 4.8.9 nodes to 5.0 first, and then add your new 5.0 cluster nodes afterward.