a) 90

b) 110

c) 160

d) 210

Correct answer is: b) 110

Formula use: a^3+b^3=\left(a+b\right)^3-3.a.b\left(a+b\right)

Explanation

Here, given expression is :
x^3+\large\frac{1}{x^3}
\rightarrow\left(x\right)^3+\left(\large\frac{1}{x}\right)^3
\rightarrow\left(x+\large\frac{1}{x}\right)^3-3.x.\large\frac{1}{x}\left(x+\large\frac{1}{x}\right)
According to the question : x+\large\frac{1}{x}\normalsize=5
\therefore\left(5\right)^3-3.x.\large\frac{1}{x}\normalsize\left(5\right)
\rightarrow\left(125-3\times1\times5\right)
\rightarrow\left(125-15\right)
\therefore 110
Ans: 110.