Let's assume the weekly allowance as 'x'.
According to the given information, Angelica spent half of one weekly allowance at the movies. So, she spent (1/2)*x = x/2 at the movies.
Then, Angelica earned $5 for cleaning the windows in the house.
Therefore, her total earnings for the week would be her allowance plus the money earned from cleaning the windows: x + $5.
Since she ended the week with $8, we can set up the equation:
x + $5 = $8
Subtracting $5 from both sides of the equation:
x = $8 - $5
x = $3
Thus, Angelica's weekly allowance is $3.