how to upgrade os x 10.5 to sierra.

Apple menu -> About this Mac should tell you what Mac you have.

If you have a PowerPC based Mac, then Leopard 10.5 is as far as you can go. If you have an intel chip set, then you can move forward.

If you can upgrade, then you will need to start with Snow Leopard, as you need Applications -> App Store to download anything newer than Snow Leopard, and Snow Leopard 10.6.6 is the first release with the App Store installed.

<http://www.apple.com/shop/product/MC573Z/A/mac-os-x-106-snow-leopard>

The Snow Leopard installation DVD will give you 10.6.3. You then need to apply the 10.6.8 combo update

<Mac OS X 10.6.8 Update Combo v1.1>

After you get to Snow Leopard, you will need to see if you can upgrade to El Capitan

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

If you qualify, then you can upgrade to El Capitan.

And from El Capitan if your Mac supports Sierra, then you can take the last step (but I seriously doubt your Mac supports Sierra - it is possible, but unlikely)

If you cannot upgrade to El Capitan, then chances are Mac OS X Lion 10.7 is as far as you can go.

No matter what you choose to do, if you go past Snow Leopard, you will mot likely need more RAM. Snow Leopard was the last release that ran well on less RAM. Everything else is RAM hungry.

Computer Compatibility - Lion Lion

Check that your computer is compatible with Mountain Lion/Mavericks/Yosemite/El Capitan.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

iMac (Mid 2007 or newer) model number 7,1 or higher

Your Mac needs:

OS X v10.6.8 or OS X Lion already installed

2 GB or more of memory (More is better - 4 GB minimum seems to be the consensus)

8 GB or more of available space

Check to make sure your applications are compatible. PowerPC applications are no longer supported after 10.6.

Application Compatibility

Applications Compatibility (2)

El Capitan 10.11 Compatibility information

macOS Sierra 10.12: Compatible Apps

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

macOS 10.12 (Sierra) requires one of the following Macs:

iMac (Late 2009 or later) Model 10.1 and higher

As well as:

Mac OS X version 10.7.5 or later

2GB of RAM (4GB minimum is more realistic)

9GB of free disk space

How to get macOS Sierra

I would assume your iMac wouldn't support Sierra if its running 10.5.

What iMac are you using?