Taxicab(n) exists (Hardy and Wright, 1938)

Taxicab(5) (Wilson, 1997) 48988659276962496 = 387873³ + 3657573³ = 1078393³ + 3627533³ = 2052923³ + 3429523³ = 214243³ + 3365883³ = 2315183³ + 3319543³

Taxicab(6)? 99% probability = 24153319581254312065344 (Rathbun, 2002; Calude, Calude and Dinneen, 2003)

Are there any numbers that are a sum of two fifth powers in two ways?