I have OS 10.5.8. Can I update to new OS? If so, what are the steps?

Purchase Snow Leopard install DVD from Apple

Then update to 10.6.8 to get App Store

From App Store download and install Yosemite

Backup first

Back up your data, click here, and read the entire page. Mac OS X 10.7 and newer don't support PowerPC software such as Microsoft Office 2004; some other installed software may also be incompatible.

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You are welcome