Which NVIDIA CUDA version works with Linux Mint 21,22, which kernel and driver?

I want to try to use GPU in my old laptop with Linux Mint 21 (kernel 5.15.0-41-generic, based on Ubuntu jammy). Trying to get NVIDIA driver and CUDA working I've found out already: 1) can install with some script or from repos. I've been installing from repos. 2) for NVIDIA driver to work after boot one can (need to?) blacklist nouveau driver - done via module_blacklist=nouveau in boot command. 3) "open" drivers work for Turing and later, not my Maxwell. So I've installed latest (not -open) from LM 21 repos: apt-get install nvidia-driver-550 nvidia-cuda-toolkit and apt downloaded 11.5 cuda files with it. 4) nvidia-smi shows the card and CUDA 12.4. Even as my debs were 11.5, why btw? But CUDA samples fail with unknown error, Web search found it could be due to: 1) too new a kernel, solution - switch to LTS. (https://bbs.archlinux.org/viewtopic.php?id=260036) 2) version (presumably kernel/driver/cuda) issues, solutions: downgrade nvidia driver / cuda. (https://discussion.fedoraproject.org/t/cuda-initialisation-errors/98985) I'm already tired of installing and booting. Please tell me which modern versions are compatible/working. Preferably for my preferred distro - Linux Mint.