Final answer:
The Beta (β) value for an NTC thermistor cannot be determined with the information provided as the question lacks sufficient data on resistance at specific temperatures or a clear relation between the given parameter (K500) and the Beta value.
Step-by-step explanation:
The characteristic temperature, commonly referred to as the Beta (β) value of an NTC thermistor, is a parameter that indicates how the resistance changes with temperature. To find this β value for an NTC thermistor with a resistance of 5000 ohms, one would typically use the Beta equation that relates the resistance of the thermistor at two different temperatures (T1 and T2) along with the resistance at those temperatures (R1 and R2). However, the question seems incomplete as it provides a parameter, K500 = 3.366 x 10^-7, but does not detail how it is related to the Beta value or provide the necessary resistances at the different temperatures. Without additional information, it is not possible to accurately determine the Beta value of the thermistor.