Hi KatyAppleton1, Thanks for the note. There is a limit on export/analysis extent on this global service as you mentioned, which is clearly stated on Terrain item page near the bottom and we can elevate that information.
“This layer allows query, identify, and export image requests. The layer is restricted to a 5,000 x 5,000 pixel limit in a single request.”
The Terrain service is comprised of global sources of various resolution (see Elevation Coverage Map) and depending upon the analysis need, one can filter a particular resolution. The limit of 5000 rows x 5000 columns means that if the resolution chosen for analysis is 10m, then the analysis limit would translate to 50,000 m x 50,000 m. As you are interested in CGIAR SRTM, which is ~90m, the maximum analysis limit would be 450 km x 450 km.
You can check out UC presentation below, which covers performing analysis with Terrain layer in desktop environment. Analysis with ArcGIS Pro section is from 12:30 - 26:00 minutes in the video.
https://mediaspace.esri.com/media/t/1_ofro14se
For North America, we have USGS 1 arcsec (~30m), which has higher limit of 24000 x 24000 if that’s of interest. There is also GMTED 7.5 arc sec (~250m) available in the Living Atlas
There are many other elevation layers available on Living Atlas from various authoritative providers that you can check out: https://livingatlas.arcgis.com/en/browse/#d=2&categories=Elevation+and+Bathymetry&type=layers
Hope this helps!