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Choice A is correct. It's given that the function $f$ is defined by $f\left(x\right)=5x+8$. Substituting $58$ for $f\left(x\right)$ in this equation yields $58=5x+8$. Subtracting $8$ from both sides of this equation yields $50=5x$. Dividing both sides of this equation by $5$ yields $10=x$. Therefore, the value of $x$ when $f\left(x\right)=58$ is $10$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the value of $f\left(58\right)$, not the value of $x$ when $f\left(x\right)=58$.