Mac os x 10.5.8

What OS you can upgrade to is governed by what mac model and year it is.

First you would need to upgrade to Snow Leopard so you will need to

buy a DVD of that somewhere. This will probably install version 10.6.3.

Next you have to upgrade that to version 10.6.8 which you can download

from here.

https://support.apple.com/kb/dl1400?locale=en_GB

Once downloaded double-click to install.

Then go to the App Store Updates page and see if there any other

updates that need to be applied.

If you want and are able to upgrade further read the following.

Read Section 1 in all of the How To articles to see if your mac can upgrade,

start with El Capitan, as I think your mac will be too old to upgrade further.

The model and year of your Mac will determine which macOS you can upgrade to,

Please use Safari to access the following links do not use Firefox

How to upgrade to macOS Mojave - Apple Support

How to upgrade to macOS High Sierra - Apple Support

How to upgrade to OS X El Capitan - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS ******.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates. 

How to upgrade to macOS Catalina – Apple Support

From Menu : About this Mac panel, what is the Mac product description line including the content in parenthesis? What is your RAM (memory) configuration line? Do not post your serial number here.

OS X Leopard 10.5.8 was released in Aug 2009, which is the first month that Snow Leopard (10.6.0) was released. Your Mac may be 12+ years old at this point, so do not count on any upgrade that is still covered by Apple security and Safari browser updates. You will be upgrading old with old.