1. The problem is to evaluate the expression $$\left(\frac{1}{x}+x\right)^8$$ when $k=5$.\n\n2. However, the variable $k$ does not appear in the expression, so we assume you want to evaluate the expression at $x=5$.\n\n3. The expression is $$\left(\frac{1}{x}+x\right)^8$$. This means we first calculate $\frac{1}{x}+x$ and then raise the result to the 8th power.\n\n4. Substitute $x=5$ into the expression:\n$$\frac{1}{5} + 5 = 0.2 + 5 = 5.2$$\n\n5. Now raise $5.2$ to the 8th power:\n$$5.2^8$$\n\n6. Calculate $5.2^8$ step-by-step or use a calculator:\n$$5.2^8 = 5.2 \times 5.2 \times 5.2 \times 5.2 \times 5.2 \times 5.2 \times 5.2 \times 5.2 = 390625.305856$$\n\n7. Therefore, the value of the expression when $x=5$ is approximately $$390625.31$$.