SQL Server Management Studio SSMS tries to "save to file" instead of execute on F5

It sounds like you have accidentally changed from the default query option of "Results to Grid" to "Results to File". If that is the case it is easy to fix:

From the Query Menu -> Results To -> Results To Grid.

OR

Press Ctrl + D

Once you have tried one of the steps above, run your query again by pressing F5.

Previous answer didn't apply to me. My query results were set to grid already (CTRL+D).

The issue is, if you're using a Microsoft ergo keyboard and the function lock (key to the right of F12 usually) is not on, then F5 will bring up an open file dialog by default.

So, yet another embarrassing resolution is: Keep F lock on! :)