Mean of TransformedDistribution returns wrong result

I want to compute the mean of this transformed distribution $10^{(25+5x+y)/5}$, where $x$ and $y$ are independent normal random variables.

Here is my code

oneStepDist = 
  TransformedDistribution[10^(
   1/5 (25 + 5 x + y)), {x [Distributed] 
     NormalDistribution[71273/100000, 11/6250], 
    y [Distributed] NormalDistribution[-4811/250, 21/500]}];
twoStepDist = 
  TransformedDistribution[10^t, t [Distributed] #] &@
   TransformedDistribution[
    1/5 (25 + 5 x + y), {x [Distributed] 
      NormalDistribution[71273/100000, 11/6250], 
     y [Distributed] NormalDistribution[-4811/250, 21/500]}];

I found Mean[oneStepDist] returns $0$ while N@Mean[twoStepDist] gives correct result $73.1164$. Is this a bug or I’m missing something?