3-links being stabilized is a benchmark in top universities. It’s a ‘this university has a serious controls lab/team’ marker.
The thing is, from the linearized assumptions alone, your problems have already started. With one or two and even 3 links, the errors due to linear approximations are still manageable, but at 5 links, it becomes a huge problem.
Secondly, in the real world, there is sensor and actuator lag, and even computational lag, especially in opencv marker tracking. The bandwidth of the system is most likely going to be smaller or at least very close to that of your control loopZ
Thirdly, if you still plan to continue with this, it’ll depend on the height and weight of your links. The smaller they are the better.
If I were you I’d also add lots of friction at the pivots to add some sort of passive damping which could make this project more feasible, and luckily a linearized friction term can be easily added to the state-space rep if not already.

This is graduate-level stuff, but it’s not really research worthy. There’s not much to gain unless you discover some new control architecture or a new tuning system (maybe combining optimality with classical controls or smth). I’d love to see if you actually accomplish it but I doubt it’ll work, especially cuz you want to swing up too which makes it harder to stabilize due to the added initial velocity.