If I have a patient with severe asthma, facial flushing, and elevated serum 5-HIAA, could this be carcinoid syndrome?

It can be carcinoid syndrome. How high is the 5-HIAA and was the urine collected on a serotonin-free diet?  If it was more than just slightly elevated, then confirm its significance by testing blood serotonin, which should be increased; blood tryptophan, which should be decreased; and chromogranin, A which should be increased. If one or two of these are clearly abnormal, you should check the liver for metastatic tumor - by CT scan with contrast or MRI. If negative, do an OctreoScan to search for tumor foci not seen by the other imaging techniques.