【Answer】26334
Analysis: $25+5=30$, this problem is equivalent to selecting 5 numbers from the 30 numbers ranging from 1 to 30, with the difference between any two numbers being at least 3. Since there are 5 numbers and 4 intervals, $30-2 \times 4=22$, thus $C_{22}^{5}=\frac{22 \times 21 \times 20 \times 19 \times 18}{5 \times 4 \times 3 \times 2 \times 1}=26334$ ways.
15. Arrange teachers A, B, C, D, E in a row with 25 identical seats, after which 25 students will sit in the seats to take photos with the teachers. Requirements: A, B, C, D, E must appear from left to right in alphabetical order, and there must be at least two seats between each adjacent pair of teachers. Then there are $\qquad$ different arrangement methods (Note: The arrangement refers to the placement of teachers and empty seats, not the subsequent seating of students).