For Elementary OS 5.1 you need to update your kernel like this
Check your kernel version
$ uname -r
4.15.0-72-generic
Update your kernel
$ sudo apt install --install-recommends linux-generic-hwe-18.04 xserver-xorg-hwe-18.04
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following additional packages will be installed:
linux-headers-5.0.0-37 linux-headers-5.0.0-37-generic linux-headers-generic-hwe-18.04 linux-image-5.0.0-37-generic linux-image-generic-hwe-18.04
linux-modules-5.0.0-37-generic linux-modules-extra-5.0.0-37-generic xserver-xorg-core-hwe-18.04 xserver-xorg-input-all-hwe-18.04 xserver-xorg-input-libinput-hwe-18.04
xserver-xorg-legacy-hwe-18.04 xserver-xorg-video-all-hwe-18.04 xserver-xorg-video-amdgpu-hwe-18.04 xserver-xorg-video-ati-hwe-18.04 xserver-xorg-video-fbdev-hwe-18.04
xserver-xorg-video-intel-hwe-18.04 xserver-xorg-video-nouveau-hwe-18.04 xserver-xorg-video-qxl-hwe-18.04 xserver-xorg-video-radeon-hwe-18.04
xserver-xorg-video-vesa-hwe-18.04 xserver-xorg-video-vmware-hwe-18.04
Suggested packages:
fdutils linux-hwe-doc-5.0.0 | linux-hwe-source-5.0.0 linux-hwe-tools xfonts-100dpi | xfonts-75dpi firmware-amd-graphics xserver-xorg-video-r128 xserver-xorg-video-mach64
firmware-misc-nonfree
Recommended packages:
xserver-xorg-input-wacom-hwe-18.04
The following packages will be REMOVED:
xserver-xorg xserver-xorg-core xserver-xorg-input-all xserver-xorg-input-evdev xserver-xorg-input-libinput xserver-xorg-input-wacom xserver-xorg-legacy
xserver-xorg-video-all xserver-xorg-video-amdgpu xserver-xorg-video-ati xserver-xorg-video-fbdev xserver-xorg-video-intel xserver-xorg-video-nouveau
xserver-xorg-video-qxl xserver-xorg-video-radeon xserver-xorg-video-vesa xserver-xorg-video-vmware
The following NEW packages will be installed:
linux-generic-hwe-18.04 linux-headers-5.0.0-37 linux-headers-5.0.0-37-generic linux-headers-generic-hwe-18.04 linux-image-5.0.0-37-generic linux-image-generic-hwe-18.04
linux-modules-5.0.0-37-generic linux-modules-extra-5.0.0-37-generic xserver-xorg-core-hwe-18.04 xserver-xorg-hwe-18.04 xserver-xorg-input-all-hwe-18.04
xserver-xorg-input-libinput-hwe-18.04 xserver-xorg-legacy-hwe-18.04 xserver-xorg-video-all-hwe-18.04 xserver-xorg-video-amdgpu-hwe-18.04 xserver-xorg-video-ati-hwe-18.04
xserver-xorg-video-fbdev-hwe-18.04 xserver-xorg-video-intel-hwe-18.04 xserver-xorg-video-nouveau-hwe-18.04 xserver-xorg-video-qxl-hwe-18.04
xserver-xorg-video-radeon-hwe-18.04 xserver-xorg-video-vesa-hwe-18.04 xserver-xorg-video-vmware-hwe-18.04
0 upgraded, 23 newly installed, 17 to remove and 0 not upgraded.
Need to get 69,9 MB of archives.
After this operation, 331 MB of additional disk space will be used.
Do you want to continue? [Y/n]
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reboot your Elementary OS
$ reboot
check your kernel version
$ uname -r
5.0.0-37-generic
Here the result with about :