An Ext.ux.DateTimeField control has been floating around on the Sencha forums. There were some patches to make it work for 5.1.
I got the latest version, renamed the class to be more like the current Ext 5.1 schema, and fixed an error when trying to select the time control.
Obsolete code was also removed.
The time control spinners do not get focus when you click in the corresponding input field. Pressing tab does focus the controls though.