Final answer:
The total number of possible 5-character passwords using letters and numbers is 62^5, and the entropy in bits is found by taking the logarithm base 2 of that total number.
Step-by-step explanation:
To solve this problem, we need to calculate the total number of possible combinations for a 5-character password. Since the password is case-sensitive and can include letters and numbers, we have 26 lowercase letters, 26 uppercase letters, and 10 digits, which totals 62 possible characters for each position in the password. Therefore, for a 5-character password, the total number of possible passwords would be 62^5.
To find the bits of entropy, we use the formula entropy = log2(n), where n is the number of possible passwords. Plugging in our number of possibilities:
entropy = log2(62^5).
The value of 62^5 can be calculated, and then the logarithm base 2 of that number gives us the entropy in bits.