I got the update Kernel notification update 5.15.0-50.56 yesterday and promptly installed it. On restart, it wouldn't start up. I reverted to a previous kernel with advanced options from Grub, all OK. Anyone else had issues?

What OS?
What hardware?
Did you have any error messages?
Can yo be anymore vague with your post?

Hello Uteck,
I'm a relative newbie here (3 years with Linux)
I'm running Linux Mint Vanessa 21 on a custom built PC. It's a Gigabyte model: Z97X-Gaming 3 v, Intel Xeon quad core i7 E3-1200 v3/4th Gen Processor, NVIDIA GK104 [GeForce GTX 770] graphics card 16GB ram and 5TB storage. My OS is on a 1tb solid state Kingston drive. It is currently running well with the 48 version kernel, but when I updated to 50, it simply would not start. No error messages. The light for the hard drive started, my monitor flashed up the usual IIyama logo, then went blank. The monitor normally has a steady blue light when in use, but the monitor dropped back to standby.

Kernel info as it is now - Kernel: 5.15.0-48-generic x86_64 bits: 64 compiler: gcc v: 11.2.0 Desktop: Cinnamon 5.4.12
tk: GTK 3.24.33 wm: Mutter dm: LightDM Distro: Linux Mint 21 Vanessa base: Ubuntu 22.04 jammy

I assume that when you boot the updated kernel you just get a blank screen? If so, yo can press the ESC key to bring up the scrolling text of the boot process, assuming the system is not totally locked up yet.
You may just have an issue starting the GUI.

Would you list the files you installed when it failed? I'm wondering if you installed everything you need for the new kernel to work. I don't run Mint, so I'm unfamiliar with the packaging.

On a new kernel you would need the modules for that kernel, headers.

Did you update grub after the kernel install?

I did get a list of the headers.
Linux-headers 5.15.0-52
Linux-headers 5.15.0-52-generic
Linux-images 5.15.0-52-generic
Linux-modules 5.15.0-52-generic
Linux-modules extra 5.15.0-52-generic

I have restored back to Kernel 48 and done an update to 5.15.0-52.58 with the same result. No start up (Although it did start once, but it was REALLY slow, and seemed slow to start up from standby)

Did you generate a new initrd.gz file after the upgrade, befire the first re-boot into the new kernel?

I was thinking this was an odd question, then I see you are using Slack so are not familiar with 21st century Linux.
Mint will do that automatically, which the OP is using, as will most every update tool out there.

The OP still needs to post what if any error can be seen on the other kernel. Clearly the GUI is not starting, but still has not tried pressing ESC at boot to see all the boot text and where it is hanging.

Never had to generate a new initgr.gz with linux mint, just did the update. Don't know what that is

Mint does that for you, so no need to manually do it.
You can watch the boot process of the kernel by pressing the ESC key right away when you boot to switch to the text screen. If that does not give you an error to work with, there is the boot log you could check in /var/log/boot.log that might give you an idea of what the problem is.