To solve the limit:

$\lim_{x \to 2} (x^3 + x^2 + 5)$

we can directly substitute $x = 2$ into the expression since it is a polynomial and continuous at $x = 2$.

$= (2^3 + 2^2 + 5)$

First, calculate each part:

$2^3 = 8, \quad 2^2 = 4$

Now sum them up:

$8 + 4 + 5 = 17$

Thus, the limit is:

$\lim_{x \to 2} (x^3 + x^2 + 5) = 17$

Do you have any questions or would you like further details?

Here are 5 related questions:

1. What is the limit of $\lim_{x \to 3} (x^3 + x^2 + 5)$?
2. How would you find the limit if the function was not continuous?
3. What happens to the limit if the polynomial included a negative term?
4. Can limits exist for non-polynomial functions at given points?
5. How can we use L'Hopital's Rule for more complex limits?

Tip: For continuous functions like polynomials, the limit can be found simply by direct substitution of the value.