How do I upgrade my MAC OS 10.5 MACBOOK to Current OS?

You can't. The maximum OS a MacBook running 10.5.8 can possibly be upgraded to is El Capitan; this requires installing Snow Leopard, updating to 10.6.8, and then getting El Capitan from the Mac App Store.

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There are three MacBook models matching those specifications, but none of them can be upgraded past Lion 10.7.5. To upgrade, buy a Snow Leopard DVD and a download code for Lion from the online Apple Store, and more RAM from a source such as Crucial or OWC.

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To avoid misunderstanding of potential replies you also need to know

more about your MacBook build model series and year introduced.

There are published online resources, here's one of a few I've bookmarked:

• Lookup Mac Specs by Serial Number, Order, Model & EMC Number, Model ID ~ EveryMac.com

https://everymac.com/ultimate-mac-lookup/

Another that can tell the year, month, and build date it left a factory; plus specifications:

• Mac Serial Number Info - Lookup your Apple Serial Number - powerbookmedic

https://www.powerbookmedic.com/identify-mac-serial.php

Because these are not simply copy-paste - each set/step of details seen above are posted manually.

Another resource if you have identified your Mac; seen what kind of hardware upgrade it may use

(not update) check into 'Verified Upgrades for your Mac' ~ you needn't register @ OWC to use this.

Hi,

You need to upgrade to El Capitan first to upgrade Mojave, though not sure your MacBook is supported with Mojave.

What is your MacBook model?

Just to add to Niel's response: You can get Snow Leopard here for $19.99: Mac OS X 10.6 Snow Leopard - Apple

Before you do anything. upgrade the ram. the newer versions need at least 4GB of ram to run. But 8gb makes a little smoother. Ram sticks are cheap at your local electronic store

Are you sure you are running 10.5? That's an incredibly old macOS version around 12 years old.

What model of Mac do you have exactly?

If you go the Apple Menu->About This Mac->More Info, tell us what Mac model it says you have there, and verify the macOS version.

More details here: Find the model name and serial number of your Mac - Apple Support

You do not even know which model the Macbook he is running. If he said which kind of model Macbook he was running. We would know what answer to tell him.

if it was made in '09. You are out of luck. https://support.apple.com/kb/SP777?locale=en_US

He would only need to upgrade to at least 2 GB to run Lion.

A Mid 2007 MacBook can only read up to 3 GB.