Each term is obtained by: previous term × position - position^2. Starting from 5200: 5200×2-4=5196, 5196×3-9=5179, 5179×4-16=5170 (should be 5186), 5186×5-25=5145. Following this pattern: 5145×6-36=5109.
The differences between consecutive terms are -1, -4, -9, -16, -25 (perfect squares 1,4,9,16,25), so the next difference is -36, giving 5145 - 36 = 5109.