It may be important to assess if you really have a throat infection
or something else. Also since you have had a recurrence in a few weeks it is important that some investigations be carried out. Based on the impression gained from the tests the appropriate management can be initiated. There is no harm in continuing amoxicillin
for 5 days again but you cannot be sure if that will resolve your problem and also repeated use of antibiotic unnecessarily may make it ineffective for you in the future.