What's Next?

5-1=4=2^2

32-5=27=3^3

288-32=4^4

3413-288=5^5

hence next number is 3413+ 6^6=5009

This is the pattern.

$1$

$5=2^2+1$

$32=3^3+5$

$288=4^4+32$

$3413=5^5+288$

$50069=6^6+3413$

1=1 5=4+1=2 2 32=5+27=3 3 3 288=32+256=4 4 4 4 3413=3125+288=5 5 5 5 5 50069=46656+3413=6 6 6 6 6*6

(1^1) = 1

(1^1) + (2^2) = 5

(1^1) + (2^2) + (3^3) = 32

(1^1) + (2^2) + (3^3) + (4^4) = 288

(1^1) + (2^2) + (3^3) + (4^4) + (5^5) = 3413

(1^1) + (2^2) + (3^3) + (4^4) + (5^5) + (6^6) = 50069

$\boxed {50069}$ is the answer