Dead thermister or dead board on Ender 5?
&quot;Heater core&quot; wires are not the same as thermistor wires, are they?
Check if thermistor is properly connected?
Reading -14 C in my case always pointed a disconnection of thermistor. (I didn't had a case of broken one so far.) In case of short it would probably show som max temperature (my guess, I dont want to try), but it is always good to check if wires are do not touch each other and are properly insulated?
Measure thermistor's resistance
If you are able to use multimeter, then:

disconnect thermistor from the printer board
set multimeter to resistance measurement (200k Ohms)
connect thermistor and multimeter using wires - the ones having aligator clips would be the best
read resistance measurent

My spare shows 97k Ohms in room conditions. So value should be high (you may refer to specs sheet of given type when in doubt).
Check that hotend is actually powered
If thermistor is OK, then indeed the hotend powering may be broken. Ths definitely require skills and may introduce many risks to electronics and maybe even to your health - but if you are skilled enough, you may measure with voltmeter if there is correct voltage provided to the hotend. For example the MOSFET on the board may be broken (I already replaced one in the past for my heated bed).