Say, LHS=f(x) & RHS=g(x).
f(x) is positive for all real x.
g(x) is positive for x>1001/3 (nearly 4.65)
f(x) can intersect g(x) for x>4.65
x=5 is the solution. Beyond 5 any other point of intersection looks unlikely as there is steep rise behavior of g(x).