Question 1180565
I would graph it first. Clearly +oo is the upper bound 
{{{graph(300,300,-10,10,-600,100,x^4-8x^3-16x+5)}}}
We know that when x=0 y=5, and as x increases from 0, the function will be decreasing, since subtracting the cube of a small positive number and the first power of a small positive number will both be larger than the adding the fourth power of that number.
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So one root will be between 0 and 1, closer to 0
when x=8, the x^4 and -8x^3 terms will cancel, making the function -123. Therefore, the next root will be somewhat larger than 8 and well below 9 (closer to 8).
The other two roots will be complex.
The critical values are at x=0.2996 and x=8.227. The function is continuous.
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The derivative is y'=4x^3-24x^2-16
set that equal to 0 and divide by 4, and the is x^3-6x^2-4=0
this is negative when x=6 and positive when x=7, so the local minimum is when x is in between those two points.
x=6.11
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So the range is (-523.8679, +oo)