Subclinical Hypothyroidism: This condition is characterized by elevated TSH levels with normal free thyroxine (FT4) levels. Given the patient's age and the laboratory values provided (TSH 5.50, which is slightly elevated, and FT4 16, which is within the normal range), subclinical hypothyroidism is a common and likely diagnosis. It often presents with mild or no symptoms, especially in the elderly.

Primary Hypothyroidism: Although the FT4 level is within the normal range, primary hypothyroidism could be considered if the patient has symptoms suggestive of hypothyroidism or if there are other laboratory abnormalities. The slightly elevated TSH could indicate a trend towards hypothyroidism.
Thyroid Hormone Resistance: A rare condition but could be considered if there are elevated TSH and normal to elevated FT4 levels without symptoms of hypothyroidism or hyperthyroidism.

Pituitary Disease (e.g., Pituitary Adenoma): Although less likely, pituitary diseases can cause elevated TSH levels due to the secretion of TSH by a pituitary adenoma or due to the compression of the normal pituitary tissue leading to decreased negative feedback and thus elevated TSH. Missing this diagnosis could have significant consequences.
Medication-Induced Thyroid Dysfunction: Certain medications can affect thyroid function tests. It's crucial to review the patient's medication list to identify any potential culprits that could be causing the abnormal TSH level.

TSH-Secreting Pituitary Adenoma with Peripheral Resistance to Thyroid Hormone: This is a very rare condition where a pituitary adenoma secretes TSH, and there is also peripheral resistance to thyroid hormone, leading to elevated TSH and normal to elevated FT4 levels.
Familial Dysalbuminemic Hyperthyroxinemia (FDH): A rare condition characterized by abnormal thyroid hormone binding proteins, leading to altered thyroid function tests without actual thyroid disease. However, this typically presents with elevated total T4 and T3 levels but normal FT4 and T3 levels.