Understanding the Problem
To find the number of even numbers greater than 300 that can be formed using the digits 1, 2, 3, 4, and 5 without repetition, we need to consider both the constraints of the number and the available digits.

Step-by-Step Breakdown
- **Even Numbers**: The last digit must be an even digit. From the available digits, the even digits are 2 and 4.
- **Condition of Being Greater Than 300**: The first digit must be 3, 4, or 5.

Case 1: Last Digit is 2
- **First Digit Choices**: Since the number must be greater than 300, the first digit can be 3, 4, or 5.
- **First Digit = 3**: Remaining digits are 1, 4, 5.
- Choices for the second digit = 3 (1, 4, 5).
- Total combinations = 3! = 6.
- **First Digit = 4**: Remaining digits are 1, 3, 5.
- Choices for the second digit = 3 (1, 3, 5).
- Total combinations = 3! = 6.
- **First Digit = 5**: Remaining digits are 1, 3, 4.
- Choices for the second digit = 3 (1, 3, 4).
- Total combinations = 3! = 6.
- **Total for Case 1**: 6 + 6 + 6 = 18.

Case 2: Last Digit is 4
- **First Digit Choices**: The first digit can again be 3, 4, or 5 but since 4 is the last digit, it cannot be the first digit.
- **First Digit = 3**: Remaining digits are 1, 2, 5.
- Choices for the second digit = 3 (1, 2, 5).
- Total combinations = 3! = 6.
- **First Digit = 5**: Remaining digits are 1, 2, 3.
- Choices for the second digit = 3 (1, 2, 3).
- Total combinations = 3! = 6.
- **Total for Case 2**: 6 + 6 = 12.

Final Count
- **Total Numbers**: 18 (Case 1) + 12 (Case 2) = 30.
Thus, the number of even numbers greater than 300 that can be formed is **30**.
**None of the provided options are correct.**