Set up a system of equations. Let $g$ be the cost of a gourmet chocolate and $p$ be the cost of a premiere chocolate.

$5g + 10p = 30.35 \quad \text{(1)}$ $6g + 6p = 22.68 \quad \text{(2)}$

Simplify equation (2) by dividing by $6$:

$g + p = 3.78 \quad \Rightarrow \quad g = 3.78 - p$

Substitute into equation (1):

$5(3.78 - p) + 10p = 30.35$

$18.90 - 5p + 10p = 30.35$

$5p = 11.45$

$p = 2.29$

Then $g = 3.78 - 2.29 = 1.49$.

The cost of $2$ gourmet and $1$ premiere chocolate:

$2(1.49) + 2.29 = 2.98 + 2.29 = \$5.27$