If my daughter is allergic to yellow dye #5, does that make her more likely to be allergic to aspirin?

Yellow dye. Tartrazine. Also known as fd&c yellow #5, tartrazine has been suspected as the cause of many reactions. Recent studies have disproven the thought that aspirin-allergic asthmatics were especially sensitive to tartrazine.
Slightly more likely. In years past, allergy to yellow dye #5 (tartrazine) was believed to cross-react with allergy to Aspirin in about 10% of the cases. Reactions can be hives (itchy, raised welts), asthma symptoms (wheezing), etc... More recent information says the cross-reactions are less common, around 2%. That means that out of 100 people allergic to yellow #5, about 2 of them will also be allergic to aspirin.