Let's simplify the expression:

$x^2 + 6 - 3x^2 + 5$

First, combine the $x^2$ terms:

$x^2 - 3x^2 = -2x^2$

Now, combine the constant terms:

$6 + 5 = 11$

So the expression simplifies to:

$-2x^2 + 11$

The simplified expression is:

$\boxed{-2x^2 + 11}$

Would you like further details on the steps or clarification?

Here are 5 related questions you might consider:

1. How do you simplify expressions with variables and constants?
2. What are like terms, and how do you combine them?
3. How do you factor quadratic expressions like $-2x^2 + 11$?
4. Can this expression be solved for a particular value of $x$?
5. How do constants affect the graph of a quadratic expression?

Tip: Always group like terms (terms with the same variable and exponent) before simplifying.