Let's solve the expression step by step:
$$3 - (+2 \frac{1}{2}) + (-3 \frac{1}{3}) - (-1) - (+5) =$$
First, convert the mixed numbers to improper fractions:
$$2 \frac{1}{2} = \frac{2*2 + 1}{2} = \frac{5}{2}$$
$$3 \frac{1}{3} = \frac{3*3 + 1}{3} = \frac{10}{3}$$
Now, substitute these values into the expression:
$$3 - (+\frac{5}{2}) + (-\frac{10}{3}) - (-1) - (+5) =$$
$$3 - \frac{5}{2} - \frac{10}{3} + 1 - 5 =$$
Group the whole numbers:
$$3 + 1 - 5 - \frac{5}{2} - \frac{10}{3} =$$
$$-1 - \frac{5}{2} - \frac{10}{3} =$$
Find a common denominator for the fractions (which is 6):
$$-1 - \frac{5*3}{2*3} - \frac{10*2}{3*2} =$$
$$-1 - \frac{15}{6} - \frac{20}{6} =$$
Combine the fractions:
$$-1 - \frac{15+20}{6} =$$
$$-1 - \frac{35}{6} =$$
Convert -1 to a fraction with a denominator of 6:
$$-\frac{6}{6} - \frac{35}{6} =$$
Combine the fractions:
$$\frac{-6 - 35}{6} =$$
$$\frac{-41}{6} =$$
Convert the improper fraction to a mixed number:
$$-6 \frac{5}{6}$$
So, the final answer is:
$$
3 - (+2 \frac{1}{2}) + (-3 \frac{1}{3}) - (-1) - (+5) = -6 \frac{5}{6}
$$
Answer: $$-6 \frac{5}{6}$$