5. (10 points) The smallest natural number that has exactly 20 divisors is ( )
A. 120
B. 240
C. 360
D. 432
【Analysis】First, decompose 20 into the product of several numbers, use the method of finding the number of divisors, starting from the smallest prime factor 2, and increase in sequence to find the answer.

【Solution】Solution: $20=20=2 \times 10=4 \times 5=2 \times 2 \times 5$;
The smallest natural numbers in the four cases are: $2^{19} 、 2^{9} \times 3 、 2^{4} \times 3^{3} 、 2^{4} \times 3 \times 5$, the smallest of which is the last one $2^{4} \times 3 \times 5=240$.

Therefore, the answer is: $B$.