5.4 is the currently stable kernel supported in Ubuntu 18.04 and Zorin OS 15.
This thread relates to Just Bought Zorin 15.3 Ultimate but not 16 - #2 by Aravisian
You may want to peruse Zorin OS 16, instead.
Currently, the Zorin OS 16 Beta comes with 5.8 kernel. This is highly likely to Climb once Zorin OS 16 is fully released.
When it comes to a Linux kernel - the newest is not necessarily the one you want. As the kernel number climbs upward, this means that the kernel version includes patches or additions for newer software. If you are running an older machine- those additions would mean nothing to you. The newest Kernel is also rolling release - which means it may have Fresh new Kernel bugs and issues that have yet to be ironed out.
As long as a computer works properly on an older kernel - then that is the kernel that you want. Upping to the newest, just for the sake of seeing a bigger number on your kernel, can actually lead to problems. Let the vetted kernel come to your system from the developers that have tested it in order to have the best results.
Now... That being said...
You can upgrade your kernel by installing the version that you want. While you are on Zorin 15.3 Ultimate, you should be able to install the latest kernel in Synaptic (If you need synaptic, you can install it with sudo apt install synaptic in terminal).
Open Synaptic, then click the Search button. Enter into it "linux headers" and then Select the version of the Mainline Signed Kernel you need. You will need
Linux Headers
Linux Image
Linux Modules.
You can also download .deb files of the Kernel (Four parts Total) and install them with One Terminal command easily. Just place the four .deb files into a folder by themselves, open a terminal in that folder or cd command to it, then in that terminal run sudo dpkg -i *.deb and it will automatically install all the packages in the correct order.
Once installed, reboot to test the newer Kernel. If the newer kernel enters kernelpanic or does not work properly, you can revert to the Old Kernel by holding the Left Shift key at boot to bring up the Recovery Menu, then selecting "Advanced Options", then choosing to boot from the previous kernel. Once logged in, you can uninstall the Newer Kernel.