Solve the Absolute Value Equation: |5-z| = Finding the Distance

To address the problem, we need to interpret $\left|5-z\right|$ correctly. The absolute value function essentially provides a non-negative outcome of the expression it encompasses. Conventionally, this expression is solved by considering two cases: when the expression inside the absolute value is non-negative and when it is negative. However, since there is no inequality provided and no instruction to solve for any specific case of $z$, the prompt asks to evaluate the original expression:

• Usually, the expression $\left|5-z\right|$ can be interpreted as $5-z$ if $5-z$ is non-negative or $-(5-z)$ if $5-z$ is negative.
• However, the problem seeks the rewritten expression, suggesting $5-z$ as the principal equivalent, matching the absolute functionality if the expression is positive or zero directly.

Thus, interpreting the multiple-choice options provided:

• Option 1: $5-z$ — representing the expression inside the absolute value directly.
• Option 2: $z-5$ — this would suggest a flip that is not aligned directly with expression values.
• Option 4: $-5+z$ — this option is simply a reordering and differs from option 1 structurally.

The choice reflecting the expression within the absolute value is $5-z$. Given the task involves equating the expression within the $\left|5-z\right|$ context for the options provided.

Hence, the solution, expressed directly, is simply:

$5-z$