Does repeated use (4-5x year) of antibiotics (recurrent tooth infection for 5 years) damage one's health or weaken immune system? clindamycin mostly.

No: Short courses of well tolerated antibiotics 4 or 5 times a year may favor the development of resistant organisms but usually cause no damage to your health or immune system unless the antibiotic has harmful or toxic side effects.

Didn't cure problem: Repetitive courses of antibiotic for tooth infection does not cure the infection, just limit it's spread temporarily. Danger that you can create strain of antibiotic resistant bacteria that at later time can be life threatening. Danger that the infected (abscessed) tooth can flare dangerously. Cure the infection with root canal treatment or extraction, not by reapplying bandaid.

Definitive Care: You need definitive dental care. An infection that recurs every three months for the past five years is obviously not going away with just antibiotics. Please see a dentist. Overuse of antibiotics can result in resistant strains and super infections.