5. Place 7 goldfish of different colors into 3 glass fish tanks numbered $1, 2, 3$. If the number of fish in each tank must be no less than its number, then the number of different ways to place the fish is $\qquad$ kinds.
5. 455 (1) If the number of goldfish placed in tanks 1, 2, and 3 are 2, 2, and 3 respectively, then there are $C_{7}^{2} \cdot C_{5}^{2}=210$ different ways;
(2) If the number of goldfish placed in tanks 1, 2, and 3 are 1, 3, and 3 respectively, then there are $C_{7}^{1} \cdot C_{6}^{3}=140$ different ways;
(3) If the number of goldfish placed in tanks 1, 2, and 3 are 1, 2, and 4 respectively, then there are $C_{7}^{1} \cdot C_{6}^{2}=105$ different ways. Therefore, there are a total of $210+140+105=455$ different ways.