To solve the equation \( 5(4 + c) = 20 + 5c \), we can start by distributing the 5 on the left side:
\[ 5 \cdot 4 + 5 \cdot c = 20 + 5c \]
This simplifies to:
\[ 20 + 5c = 20 + 5c \]
Now, we see that both sides of the equation are identical:
\[ 20 + 5c = 20 + 5c \]
This means that the equation holds true for all values of \( c \). Therefore, there are infinitely many solutions, and \( c \) can be any real number.