installing a backup second thermostat
I have a 120V / 20A baseboard stat that goes that low and would like to use it to over ride the T5 even if it is turned off. My concern is that if it is turned off or on and the second one over rides it will the voltage spike damage the T5? Any ideas on protecting the T5? 


You don't say whether the T5 is controlling the electric baseboard heat or some other heat system.  

If it's controlling some other heat system, there's no issue at all letting the baseboard thermostat switch separate baseboard heat on and off.  This is a pretty common setup.  

If the T5 is controlling a relay / contactor that's switching the baseboard heat, I can't see any issue that could damage the T5, but I could see it simply not working.  

If the baseboard thermostat is in series with the contacts controlled by the T5, both the T5 and the baseboard thermostat need to call for heat to turn on the baseboard.  

It's unlikely that the baseboard thermostat is in parallel with the contacts controlled by the T5 - that would be a bit of work to wire - but if that's the case, it would work as you want and it wouldn't damage the T5, or the relay / contactor.  


  I just wish the T5 would go down low enough. 


This is the real solution - swap out the T5 with a thermostat that works the way you want it to.