The problem with such calculations is that they're very sensitive to the chosen starting point: compare the growths in the most recent 3 instead of 5 years:
I ran into this problem yesterday trying to calculate changes in federal spending over time. One user claimed that inflation-adjusted spending had sharply declined between 2000 and 2010 - which was true. But I had already calculated that spending had sharply increased from 1990 to 2023. I couldn't understand how we had reached such different conclusions until I looked at the IRS data book and saw that there was a slump in 2010 (presumably due to the effects of the Great Recession) and a huge spike starting in 2020.
If we're looking for a trend that follows a specific city instead of specific year and city, then I agree. For that purpose I think I'd like to run this same calculation for the 5 year interval 2019-2024, and 2018-2023, and 2017-2022, etc, to see if there is a trend that is unique to the cities, as opposed to the cities in a certain year.
However, my interpretation of the original claim about Austin is "Austin house prices have grown less in the last 5 years than other places". That claim is pretty specific, and can be examined by looking at just the start and end points. Looking at the end points, it seems incorrect.
Austin: 502-> 510 growth: 1.6%
Dallas: 263-> 295 growth: 12.2%
NYC: 255-> 318 growth: 24.7%
SF: 349-> 361 growth: 3.4%
LA: 384-> 443 growth: 15.4%