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If your five year old recently had fever then dengue should be ruled out. The commonest cause of petechiae is a low platelet count (thrombocytopenia).
They can also result from autoimmune disorders, such as lupus or rheumatoid arthritis, bone marrow disorders such as leukemia, inflammation of the veins, as a side effect of certain medications, viral infections, such as EBV or Dengue and septicemia or infection in blood. A complete blood count, urine examination and a blood culture may be required to reach a diagnosis.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!
Like doctornee medical, I would recommend telling his parents to go to their gp and rule out anything like leukemia. If his frequent bloody noses take a while to stop bleedin and he bruises easily, it could be haemophilia (I don't know if this could cause petechiae), which it just as dangerous as leukemia if not treated. Get his parents to get him checked out.