To rewrite the right side of the equation \( 6x + 3 = 5(x + 3) \) by distributing the 5, we will apply the distributive property:
\[ 5(x + 3) = 5 \cdot x + 5 \cdot 3 \]
This gives us:
\[ 5x + 15 \]
Now, we can rewrite the equation:
\[ 6x + 3 = 5x + 15 \]
So we have:
\[ 6x + 3 = 5x + 15 \]
In summary, the rewritten right side is \( 5x + 15 \).