It has been proved by Ruffini (1799) and Abel (1826) 
that the solution of the general quintic (5th degree
equation cannot be written as a finite formula.  So 
there are no formulas for solving 5th degree equations.
Their solutions can only be approximated.  It is not 
fair to ask anyone to find the inverse of a 5th degree 
equation.  However you can sketch the inverse even 
though you cannot find its equation.

Here is the graph of  y = x^5 + 5x^3, from -2 to 2 



Even though you can't get an equation of the inverse,
you can sketch the inverse.

Draw the line y = x, called "the identity line". I'll draw it dotted in 
blue:

  

Now by freehand draw that curve's reflection in the indentity line,
I'll draw it in green.



So even though there is no way to find an equation for the inverse
function, you can by freehand sketch the graph of the inverse function
by drawing its reflection in the line y=x.

Edwin