gparted - can I increase root and other disk's size without formatting it

want to shrink home ie sda5 and expand root ie sda3

Device        Start       End   Sectors   Size Type
/dev/sda1      2048  20469759  20467712   9.8G Linux swap
/dev/sda2  20469760  28469247   7999488   3.8G BIOS boot
/dev/sda3  28469248  48939007  20469760   9.8G Linux filesystem

/dev/sda4  48939008  49133567    194560    95M EFI System
/dev/sda5  49133568 976771071 927637504 442.3G Linux filesystem

New partition

Device Start End Sectors Size Type
/dev/sda1 2048 20469759 20467712 9.8G Linux swap
/dev/sda2 20469760 28469247 7999488 3.8G BIOS boot
/dev/sda3 28469248 79622143 51152896 24.4G Linux filesystem

/dev/sda4 79622144 80670719 1048576 512M EFI System
/dev/sda5 80670720 976773119 896102400 427.3G Linux filesystem

Yes, you can do this, but it's a little more complicated.

You MUST boot from some other medium (Live USB, Live CD, network boot from your local network, ...) and run gparted. /dev/sda? MUST NOT be mounted during this process. You should have reliable power, and not be running on battery.

"Free Space" (which you will create by shrinking /dev/sda5) can only be added to adjacent partitions, so you will have to move partitions around.

All of this is from within gparted:

Select /dev/sda5.

Menu->Partition->Move/Resize will bring up a window like this

When you set the new partition size, be sure to have all of your free space in Free space preceeding.

This will create Free space between /dev/sda4 and /dev/sda5.

Select /dev/sda4 and Menu->Partition->Move/Resize.

Then, move /dev/sda4 to the other side of the "Free space" by clicking on the up-arrow in "Free space preceeding".

Finally, select /dev/sda3, Menu->Partition->Move/Resize and
adjust the "New size".

Examine the list of pending operations, double-checking for misexpressed intent. Fix as needed. When there's a match between what you want to do and what gparted is going to do, click the checkmark and stand back.