I got the following disk
sda9 contains a new Linux installation which I'd like to keep, while sda5 is the old installation which I'd like to free (and successively merge with sda4, but we don't care).
sda4 contains a Windows installation which I'd like to keep.
The question, made to be sure of avoiding (grub) problems at boot, is:
do I need just to delete sda5 without any other operation, and nothing will break ?
Be sure that you run
sudo update-grub
immediately after you make any changes to the partition table. That is not necessary in some cases but it is always safe to do it.
In your case it is better to make all changes from your new Linux installation: delete a partition and then update grub.
If you are going to use Live CD instead you need to update grub by chroot-ing to your new Linux installation (you don't need to reinstall it, only update).
That should work unless you made any unsafe changes to your configuration files (e.g., if you ever made any changes to /etc/fstab, you must check that all partitions there are identified by UUID, not by their names).
Anyway to be on the safe side it is always better to have Live CD in case something goes wrong. Good luck!
