Anemia with Thrombocytopenia: The combination of low hemoglobin (Hb 5.5) and low platelet count (56) could indicate a bone marrow failure syndrome or a condition affecting both red and white blood cell production. Sweating could be a symptom of anemia due to decreased oxygen delivery to tissues.

Chronic Blood Loss: Chronic blood loss can lead to iron deficiency anemia, which is characterized by low hemoglobin levels. The body may compensate for the loss of red blood cells by increasing heart rate and sweating to maintain oxygen delivery to tissues.
Hematologic Malignancy: Conditions like leukemia or lymphoma can affect blood cell production, leading to anemia and thrombocytopenia. Sweating can be a symptom of these conditions, possibly due to anemia or as a part of the disease's systemic symptoms.
Vitamin Deficiency Anemia: Deficiencies in vitamins like B12 or folate can lead to anemia. While thrombocytopenia is less common, it can occur, especially in severe deficiencies. Sweating might be related to the underlying metabolic disturbances.

Acute Bleeding: Although less likely given the thrombocytopenia, acute blood loss can cause a rapid drop in hemoglobin and lead to sweating due to hypovolemia and shock.
Sepsis: Sepsis can cause a consumption coagulopathy leading to thrombocytopenia and can also lead to anemia due to hemolysis or bone marrow suppression. Sweating is a common symptom in sepsis due to the systemic inflammatory response.
Hemolytic Uremic Syndrome (HUS) or Thrombotic Thrombocytopenic Purpura (TTP): These conditions are characterized by thrombocytopenia, microangiopathic hemolytic anemia, and can present with sweating among other symptoms due to the systemic nature of the disease.

Thalassemia Major: A genetic disorder affecting hemoglobin production, leading to severe anemia. While it's less likely to present for the first time in adulthood, it could be considered in areas where the disease is prevalent and if there's a family history.
Myeloproliferative Neoplasms: Conditions like essential thrombocythemia or polycythemia vera can sometimes present with thrombocytopenia due to splenic sequestration or other mechanisms, and anemia. Sweating can occur due to increased metabolic rate or as part of the disease's symptomatology.
Paroxysmal Nocturnal Hemoglobinuria (PNH): A rare, acquired, life-threatening disease of the blood characterized by the destruction of red blood cells, bone marrow failure, and the potential for thrombosis. It could present with anemia, thrombocytopenia, and sweating among other symptoms.