1 \ + \ 5 \ \cdot \ 2 \ + \ \left( 1 \ + \ 3 \right)^{2}
Starting from left to right, we first simplify the expression inside the parentheses:
\[1 + 5 \cdot 2 + (1+3)^2 = 1 + 5 \cdot 2 + 4^2\]
Next, we calculate $5 \cdot 2$:
\[1 + 5 \cdot 2 + 4^2 = 1 + 10 + 4^2\]
Then, we evaluate $4^2$:
\[1 + 10 + 4^2 = 1 + 10 + 16\]
Finally, we add the remaining numbers:
\[1 + 10 + 16 = \boxed{27}\]