Smallest 5th Power equal to Sum of 5 other 5th Powers

Theorem
The smallest positive integer whose fifth power can be expressed as the sum of $5$ other distinct positive fifth powers is $72$:
 * $72^5 = 19^5 + 43^5 + 46^5 + 47^5 + 67^5$

Proof
Let $\tuple {I, J, K, L, M}$ be the $5$ distinct positive fifth powers where $I < J < K < L < M$

The following program in R iterates through 97,330,464 calculations and verifies the assertion.

for (I in 1:19) { for (J in 2:43) { for (K in 3:46) { for (L in 4:47) { for (M in 5:67) { if (abs((I^5+J^5+K^5+L^5+M^5)^0.2 - round((I^5+J^5+K^5+L^5+M^5)^0.2)) < 0.00000001) { print(paste((I^5+J^5+K^5+L^5+M^5)^0.2, I, J, K, L, M)) } 				} 			} 		} 	} }