The expression you provided is \(5(n^2 + 2)\), where \(n \in \mathbb{N}\). This indicates that \(n\) is a natural number. Assuming you meant \(\mathbb{N}\) to refer to the set of natural numbers starting from 1 (traditionally \(\mathbb{N} = \{1, 2, 3, \ldots\}\) but sometimes includes 0 depending on the context), the expression can be simplified or evaluated for specific values of \(n\).

Let's simplify the expression first:

\[ 5(n^2 + 2) = 5n^2 + 10. \]

Now, if you want to evaluate this expression for specific natural numbers, substitute various values of \(n\):

1. \( n = 1 \)
\[ 5(1^2 + 2) = 5(1 + 2) = 5 \times 3 = 15. \]

2. \( n = 2 \)
\[ 5(2^2 + 2) = 5(4 + 2) = 5 \times 6 = 30. \]

3. \( n = 3 \)
\[ 5(3^2 + 2) = 5(9 + 2) = 5 \times 11 = 55. \]

4. \( n = 4 \)
\[ 5(4^2 + 2) = 5(16 + 2) = 5 \times 18 = 90. \]

5. \( n = 5 \)
\[ 5(5^2 + 2) = 5(25 + 2) = 5 \times 27 = 135. \]

And so on for any other natural numbers you wish to evaluate. If you have a specific question or need, feel free to clarify!