have a MacBook Pro lap top which uses 10:15-5 OS Yosemite how can I upgrade my OS system to Catalina? If i have to backup my laptop, what size external drive do I need?

You do not say what exact Mac this is...

running Yosemite you will have to stair step your way up to at least El Capitan

https://www.apple.com/macos/catalina/

https://itunes.apple.com/us/app/macos-catalina/id1466841314?mt=12&l=en-us

macOS Catalina - Technical Specifications - Apple Support

https://support.apple.com/kb/SP803?locale=en_US

System requirements macOS 10.15 Catalina

macOS Catalina will run on all Macintosh computers that supported Mojave:

MacBook: Early 2015 or newer

MacBook Air: Mid 2012 or newer

MacBook Pro: Mid 2012 or newer

Mac Mini: Late 2012 or newer

iMac: Late 2012 or newer

iMac Pro

Mac Pro: Late 2013 or newer; Mid 2010 or Mid 2012 if upgraded with a recommended Metal-capable GPU

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OS X 10.11 El Capitan - Technical Specifications:

https://support.apple.com/kb/SP728

How to upgrade to OS X El Capitan - Apple Support

https://support.apple.com/en-us/HT206886

download direct:

http://updates-http.cdn-apple.com/2019/cert/061-41424-20191024-218af9ec-cf50-4516-9011-228c78eda3d2/InstallMacOSX.dmg

MacBook (Early 2015)

MacBook (Late 2008 Aluminum, or Early 2009 or newer)

MacBook Pro (Mid/Late 2007 or newer)

MacBook Air (Late 2008 or newer)

Mac mini (Early 2009 or newer)

iMac (Mid 2007 or newer)

Mac Pro (Early 2008 or newer)

Xserve (Early 2009)

back up drive typically at least the capacity of your internal harddrive.

3-2-1 Backup Strategy: three copies of your data, two different methods, and one offsite.

Boot clone https://discussions.apple.com/docs/DOC-10081

How to use Time Machine to back up or restore your Mac: https://support.apple.com/en-us/HT201250

Use DiskUtility Restore feature https://support.apple.com/guide/disk-utility/restore-a-disk-dskutl14062/mac

note: >System Preferences>Security & Privacy >Privacy>Full Disk Access

unlock the padlock, press the + button and add Disk Utility

Hi,

I just wonder if your MacBook Pro is supported Catalina.

https://support.apple.com/en-us/HT210222

As for external drive size for backup, say TimeMachine, you would be good to have double size of internal drive size.

Does your Mac meet the requirements for Catalina (2012 or newer)?