The problem provided can be broken down as follows:

• The car company issues new ID codes for its employees.
• Each code consists of one digit followed by four letters.
• Some restrictions: The letter "V" and the digits 3, 4, and 5 will not be used.
• Thus, there are:
  • 25 available letters (since "V" is excluded from the 26 letters of the alphabet).
  • 7 available digits (since 3, 4, and 5 are excluded from the 10 digits: 0-9).

We need to calculate the total number of possible ID codes.

Steps:

1. For the digit:

   • There are 7 available digits.

2. For each letter:

   • There are 25 possible letters for each of the four letters, and they can be repeated.

Total number of codes:

• For the digit: $7$ choices.
• For each of the four letters: $25$ choices for each.

Thus, the total number of employee ID codes is calculated by multiplying these values:

$7 \times 25 \times 25 \times 25 \times 25 = 7 \times 25^4$

Let me calculate that.

$25^4 = 25 \times 25 \times 25 \times 25 = 390625$

Now, multiply by 7:

$7 \times 390625 = 2734375$

Final Answer:

The total number of possible employee ID codes is 2,734,375.

Would you like more details on any part of this calculation?

Here are 5 related questions for further exploration:

1. How would the answer change if the letters could not be repeated?
2. What if the restriction on digits 3, 4, and 5 were removed?
3. How many codes would be possible if only uppercase letters were allowed?
4. If another letter besides "V" was excluded, how would it affect the result?
5. What if the ID code required two digits followed by three letters instead?

Tip: When calculating combinations with repetition, always account for restrictions to ensure accurate results.