Where can I download ubuntu image with 5.11.0-27-generic kernel?

https://packages.ubuntu.com/focal/amd64/linux-image-5.11.0-27-generic/download

If you are running Ubuntu, it is strongly suggested to use a package manager like aptitude or synaptic to download and install packages, instead of doing so manually via this website.

You should be able to use any of the listed mirrors by adding a line to your /etc/apt/sources.list like this:

deb http://security.ubuntu.com/ubuntu focal-security main 

If your upgraded version is higher than the current kernel version, by default the newly installed kernel is started in the first order, just restart the system, otherwise, you need to modify the configuration file

vim /etc/default/grub

Modify GRUB_DEFAULT=0 to GRUB_DEFAULT="Advanced options for Ubuntu>Ubuntu, with Linux XXXX-generic", save and exit.

Note: For the old version of ubuntu (it seems to be before 16.04), GRUB_DEFAULT can be modified to the corresponding serial number. After 16.04, it should be modified to: Advanced options for Ubuntu>Ubuntu, with Linux x.x.x-x-generic.

then

update-grub && reboot