Final answer:
The infant's symptoms strongly indicate dehydration due to vomiting, and the most likely laboratory finding is hyponatremia.
Step-by-step explanation:
The clinical presentation of a 5-month-old infant with a history of vomiting, irritability, and decreased tear production suggests that she is experiencing symptoms of dehydration, likely as a result of acute gastroenteritis, which could be suggested by her sister's similar symptoms. Given that she has not had a wet diaper in 10 hours, tachycardia, and her other symptoms, the most probable laboratory finding would be hyponatremia. This occurs due to the body losing more sodium-containing fluids than water, which is common in cases of frequent vomiting and inadequate fluid intake.