To solve the equation \( 5(x + 2) = 2x + 19 \), we start by distributing the 5 on the left side:
\[ 5(x + 2) = 5x + 10 \]
Now, our equation looks like this:
\[ 5x + 10 = 2x + 19 \]
Next, we want to get all terms involving \( x \) on one side and the constant terms on the other side. First, let's subtract \( 2x \) from both sides:
\[ 5x - 2x + 10 = 19 \]
This simplifies to:
\[ 3x + 10 = 19 \]
Now, we will subtract 10 from both sides to isolate the term with \( x \):
\[ 3x = 19 - 10 \]
This simplifies to:
\[ 3x = 9 \]
Finally, we divide both sides by 3 to solve for \( x \):
\[ x = \frac{9}{3} \]
This gives us:
\[ x = 3 \]
So, the solution to the equation is:
\[ \boxed{3} \]