I added a newer version of kernels but when running advanced options with start system it shows only 5.4.0, with which elementary was installed
Updated your grub with update-grub?
So in /boot/grub/grub.cfg the kernels are stated in the menu list?
Also, when running update-grub, output shows kernel's like so:
Generating grub configuration file ... Found linux image: /boot/vmlinuz-5.0.0-37-generic
Are the installed kernels shown?
The following should be sufficient:
update-initramfs -c -k all
update-grub or grub-mkconfig -o /boot/grub/grub.cfg
When no succes, you could try: https://help.ubuntu.com/community/Boot-Repair