[math-fun] x^n + y^n = z^n + w^n

We know integer solutions of x^n + y^n = z^n + w^n, for n <= 4. For example, for n=4: http://www.research.att.com/~njas/sequences/A018786 But it seems that we do not know any nontrivial solution for n > 4. Am I right? Blair Kelly found no solution for x^5 + y^5 = z^5 + w^5 < N = 1.02 x 10^26 (Guy's UPINT, 3rd edition, p.210). Do you know some other results for n > 4? Christian.