The limit does not exist. For small enough [tex]x<0[/tex] we have [tex]x^3+1>0[/tex] and [tex]x^5<0[/tex], while for small enough [tex]x>0[/tex] we have [tex]x^3+1>0[/tex] and [tex]x^5>0[/tex]. This means to the left, the limit has negative sign, and to the right, the limit has positive sign. Direct substitution gives the undefined [tex]\dfrac10[/tex] which indicates the limit is infinite, but the sign changes depending on the direction.
