To determine how many numeric personal identification numbers (PINs) can be generated for a 5-digit PIN using the numbers 0 through 5 (which gives us 6 choices), we can use the principle of counting.
Each digit of the PIN can be any of the 6 digits (0, 1, 2, 3, 4, or 5). Since the PIN consists of 5 digits and each digit can be chosen independently from the 6 available options, we calculate the total number of possible combinations as follows:
\[ \text{Total PINs} = \text{Number of choices per digit}^{\text{Number of digits}} = 6^5 \]
Calculating \(6^5\):
\[ 6^5 = 6 \times 6 \times 6 \times 6 \times 6 = 7776 \]
Therefore, the total number of different 5-digit PINs that can be generated is 7,776.