Let the cost of one large soda be \( x \).
According to the problem, the total cost of 5 sodas is given by:
\[ 5x \]
It is also stated that this total cost is equal to the cost of 3 sodas plus 7. Therefore, we can write the equation:
\[ 5x = 3x + 7 \]
To solve for \( x \), first, we will subtract \( 3x \) from both sides:
\[ 5x - 3x = 7 \]
This simplifies to:
\[ 2x = 7 \]
Next, we divide both sides by 2 to find \( x \):
\[ x = \frac{7}{2} = 3.5 \]
Thus, the cost of one soda is:
\[ \boxed{3.5} \]