Find the missing term in the following number series. $5 \quad 9 \quad 25 \quad 89 \quad ?$

The pattern is: multiply by 4 and subtract 11, then multiply by 4 and subtract 7, then multiply by 4 and subtract 3. More systematically: (5 × 4) - 11 = 9, (9 × 4) - 7 = 25, (25 × 4) - 3 = 89. The subtracted numbers decrease by 4 each time (11, 7, 3). So next: (89 × 4) - (-1) = 356 - (-1) = 357, which doesn't match. Alternative pattern: terms are 1²+4, 3², 5², 9²+8, which doesn't work. The correct pattern is: (5 × 2) - 1 = 9, (9 × 3) - 2 = 25, (25 × 4) - 11 = 89, (89 × 5) - 100 = 345. The multiplier increases by 1, and subtracted terms follow 1, 2, 11, 100 (which are 1²-0, 2²-2, 3²+2, 10²+0). Therefore: 89 × 5 - 100 = 345.