MacOS catalina 10.15.5 update is not installing.

Try downloading and applying the macOS Catalina 10.15.5 Combo Update. It's usually easier too download and more reliable to apply.

If it still doesn't work boot into Safe Mode (How to use safe mode on your Mac - Apple Support) by booting with the Shift key held down and and try running it from there.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing some system cache cleaning, volume verifying and directory repairing. 

Ok ignore the restart prompt and just let the mac run normally.

Download the standalone Combo updater from here,

https://support.apple.com/kb/DL2040?viewlocale=en_US&locale=en_US

Once downloaded double-click to install.

When updating your mac using the System Preferences> Software Update it is

always best to use a cabled connection to your router rather than WiFi.

Do not use the mac while it is downloading and do not use any devices that share the

same internet connection as the mac while it is downloading.

I never saw this problem with my Mac but in version 10.15.5 I'm also facing same problem. My Mac has only 9GB space left, I think insufficient space is the problem, please let me know if you solve this issue,

If you only have 9 GB of free space on your boot drive that definitely is the problem. You'll need to free up an additional 15GB or more. Also you should maintain a minimum of 20 GB of free space to facilitate optimal system and application performance.

I tried doing the update with the safe mode reboot 3 times and it still didn't work. what is going on? It has never been this hard to update my computer before.

How much free space do you have on your boot drive?

Actually i only have 250gb ssd in my mac, and I'm having Xcode android studio and many development related tools, i think its time to upgrade ssd.

I believe you're right.