Can I upgrade my 2009 macbook pro from version 10.5.8? If so, how?

Also note, RAM upgrades were fairly easy as DIY in those early notebook models. Check pricing at OWC = macsales.com Don't go cheap on RAM, because Macs are picky.

Realize El Capitan is fairly old by now but still capable as long as you're not insisting upon running the latest software versions of everything.

There may be a small issue though. You're running 10.5. El Capitan and pretty much any Mac system version these days has to be downloaded from the Mac App Store using a special application. The conventional way to do this was to first upgrade from Leopard (10.5) to Snow Leopard and then download the El Capitan installer with that. Snow Leopard is no longer sold. You either have to find a copy or find a friend with a newer Mac who can create a boot drive with an installer on it. If you want to go that route that's a whole another post unto itself. :-/

Another thing. Your hard drive is almost full. You will need to clear room for El Capitan, and it is a good idea to always leave at least 15+ GB free at ALL TIMES, particularly if you only have 2 GB RAM.

The BAD news is that you need to be running 10.6.8 or later (available only by Installer DVD) to get the Mac App Store, from where you could download 10.11El Capitan.

Macs with less than 6GB of RAM have trouble with appropriately-responsive operation with El Capitan and later. Yours can support 8GB as two DIMMS @ 4GB each.

It can go as high as El Capitan.

Check if your apps will still work with El Capitan - https://roaringapps.com/apps

Back up your data - -> Back up your Mac with Time Machine - https://support.apple.com/HT201250

Upgrade to OS X El Capitan - https://support.apple.com/HT206886 - "OS X El Capitan remains available for Mac computers that can't upgrade to macOS High Sierra, or that need to upgrade to El Capitan first." Includes a direct link to El Capitan installer app. This will download a .dmg file with an installer package which you use to generate an installer app which will be placed in your Applications folder.

Note, 2 GB RAM means it will be slow with El Capitan, particularly if you use any demanding apps.

So according to Apple you're out of luck. The only thing stopping you is the Hardware, its just not compatible with the new updates and if you installed them you may not even be able to turn on the computer. Now you can search for older versions of MacOs to see if they are compatible, I'm not sure if they are able for Download but they should be.

One note when updating your MacBook, the more recent updates you install the slower response times you will get on your Mac. One of the other MacBooks I have is from 2012 and its on Catalina, Its the slowest thing ever. So just to warn you it may slow your Mac. Also if you go on the app store (if its there and works) you can find newer and older versions of MacOs.