Find a formula $a_{n}$ for the $n$th term of the arithmetic sequence whose first term is $a_{1}=-5$ such that $a_{n}-1-a_{n}=8$ for $n \geq 1$. \[ a_{n}= \]

Step 1 ：The given equation seems to be incorrect as it simplifies to \(-1=8\), which is not possible. However, if we assume that the equation is \(a_{n+1}-a_{n}=8\) for \(n \geq 1\), then it makes sense as it represents the common difference of the arithmetic sequence.

Step 2 ：In an arithmetic sequence, the nth term can be found using the formula \(a_{n} = a_{1} + (n-1)d\), where \(a_{1}\) is the first term and \(d\) is the common difference. Here, \(a_{1} = -5\) and \(d = 8\).

Step 3 ：The formula for the nth term of the arithmetic sequence is \(a_{n} = -5 + (n-1) \cdot 8\)

Step 4 ：\(\boxed{a_{n} = -5 + (n-1) \cdot 8}\)