Sequence Analysis: Is 5 an Element of n+10?

To determine if the number 5 is an element in the sequence represented by $n + 10$, we follow these steps:

• Step 1: Set up the equation. The sequence is defined by $n + 10$. We need to see if there is an integer value of $n$ such that $n + 10 = 5$.
• Step 2: Solve the equation for $n$. Subtract 10 from both sides of the equation to isolate $n$. This gives:

$n + 10 = 5$
$n = 5 - 10$
$n = -5$

• Step 3: Verify if $n$ is an integer. In this case, $n = -5$ is an integer.
• Step 4: Assess if the integer value of $n$ makes 5 an element of the sequence. We calculated $n = -5$, but substituting back into the sequence expression $n + 10$, we find that:

$n + 10 = -5 + 10 = 5$

Even though the calculation confirms the sequence expression can equal 5 when $n = -5$, the outcome of the problem requires us to examine the phrasing of determining "an element in the sequence." This means that 5 is part of the sequence set generated specifically for $n + 10$, but the negative positioning in the sequence implies interpreting within sequence starting conditions normally set for non-negative domains in standard sequences, which leads to reconsideration for inclusion in conventional practices.

Therefore, given the phrasing conventionally reviews from standard series starting methods, the final solution to the problem is No.