Probably. It depends on your total income.
The best way to find out whether you owe Arizona tax is to prepare a nonresident AZ tax return. You can do this for free in TurboTax online. If you don't owe you can delete the return before you file and TurboTax will not charge you for Arizona.
Additionally, even if you owe no tax, it's possible you will still be required to file an Arizona return. Arizona has a filing threshold, but for non-residents the level is prorated on the ratio of your AZ income / total income.
See: Income Tax Filing Requirements
Lastly, it is generally a good idea to file a tax return when property sales are involved as those are reported to the government. AZ will not know you only made $5,000 because only the sale price will be reported so they may assume you made more and ask for a tax return in the future.
I am trying to figure out exactly where I should go in Turbo tax on line to fill out the AZ NR form. I have the Deluxe on my computer but they want me to purchase it. I just want to see if I need to file rather than pay for it and not use it.