If $a$, $b$ are the roots of $x^2-2x+3$.Then the equation whose roots are $a^3-3a^2+5a-2$ and $b^3-b^2+b+5$ is: 
If $a$, $b$ are the roots of $x^2-2x+3$.Then the equation whose roots are $a^3-3a^2+5a-2$ and $b^3-b^2+b+5$ is:   

I have not been able to find a better method than to calculate $a$ and $b$ then substitute them into the roots for the new polynomial. 
I believe this question can't be transformed in a similar manner as mentioned in this question as the new roots are asymmetrical.  
Does a better method than the lackluster substitution, exist?  
The answer is:

 $x^2-3x+2$


Hint:
As $a,b$ are the roots of $x^2-2x+3=0$
$a^3-3a^2+5a-3=(a^2-2a+3)(a-1)+1=1$
Similarly for $b$
