The scaling for degrees Celsius and Kelvin are the same, its just that with Celsius, readings are offset by -273K, so it doesn't matter if its 5 less degrees. This is the same as the kelvin value, take away 5, if that makes sense.
In other words, when you took away (5+273) you actually solved an equation as though the temperature decreased by 278 degrees, which is definitely not the case!!
I recommend watching some video on YT which explains differences and similarities between Celsius and kelvin, which should help clear things up for you.