QB Issue Resolution:

You should order Quickbooks Mac 2015 – that’s the latest version and is officially supported on Apple’s Yosemite OS. Intuit has a money-back return policy. I’m not sure all outlets have it though – check where you bought it. Note you can order it online from Amazon at a discount and just download it.

All newer versions should be able to import QB Mac 5 data. That’s a really old version and not many people are importing it any more though – who knows if your data has some issue after all those years of use. Before importing it (and while still on the PowerPC Mac) first make a backup of your company file and put it in a safe place (like a CD or a USB key). Then run File->Utilities->Verify. If any problems are reported run File->Utilities->Rebuild.

After that, get your file to the new machine (again a USB key will work, or use networking). Then launch QuickBooks Mac 2015 (or 2014, but I do strongly suggest getting 2015) and launch it. It may detect an update is available – go ahead and apply that. Finally choose File->Open and select your old company file. It should upgrade. Run File->Utilities->Verify after the upgrade and, if a problem is reported, File->Utilities->Rebuild (now on the new copy of QB).

Resolution for Issue 'Problems updating from QB Pro for Mac 5.0 (circa 2002!) to QB Pro for Mac 2014?' available: Yes (Solved).
Source: Intuit Community forum.

Problems updating from QB Pro for Mac 5.0 (circa 2002!) to QB Pro for Mac 2014?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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