Low Dose Exemestane vs Low Dose Tamoxifen in Post-menopausal Women at High Risk for Breast Cancer.

Inclusion Criteria: 1. Postmenopausal state is defined as no menses for 12 months without an alternative medical cause. A high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a post- menopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient. Permanent sterilization methods include hysterectomy, bilateral salpingectomy and bilateral oophorectomy. Any of the following criteria must be met: 1. Recent (within 12 months from date of consent form signature) histologic diagnosis of ER+ve (\>5%) DCIS (patients with DCIS should have undergone breast-conserving therapy i.e. lumpectomy to remove the tumor with negative surgical margins followed by radiotherapy) or diagnosis within 3 years of HRL (ADH, LCIS, ALH), or: 2. At least 3% breast cancer risk at 5 years (or 5% risk at 10yrs) per one of the following risk models: the Breast Cancer Surveillance Consortium risk calculator V3 or Tyrer-Cuzick model V8 or: 3. Known carriers of a germline pathogenic/likely pathogenetic variant in the following moderate penetrance genes (CHEK2 or ATM), or women with chest wall irradiation before age of 30 years. 2. Eastern Cooperative Oncology Group - Performance Status (ECOG-PS) 0-1. 3. Able to swallow oral medications. 4. Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. Specifically, all cancers diagnosed since 3 years or longer except for breast and endometrial are eligible. 5. Ability to understand and the willingness to sign a written informed consent document. 6. Mammography performed up to 6 months before the trial consent form signature. 7. DEXA performed up to 12 months before the trial consent form signature. 8. Patients with life expectancy ≥ 10 years. 9. Patients with normal liver function tests and blood cell count. 10. Negative gynaecological examination performed up to 6 months before the trial consent form signature. Exclusion Criteria: 1. Pre/perimenopausal women 2. History of DVT or PE. 3. Endometrial cancer. 4. Macular disorders. 5. Inability to comply with study procedures. 6. Prior use of antiestrogens within 12 months from the date of the trial consent form signature. 7. Use of hormone replacement therapy (HRT) within 3 months from the date of the trial consent form signature. 8. Severe osteoporosis (T score ≤ 2.5 at either spine or hip), or recent vertebral fracture (within 6 months) not treated with zolendronic acid or denosumab. 9. Use of terbinafine, quinidine, cinacalcet, rifampicin, phenytonin, carbamazepine, phenobarbital, and St. John's wort, warfarin, erythromycin, cyclosporin, nifepidine and any concomitant coumarin-type anticoagulant therapy. 10. Patients with moderate or severe renal impairment. 11. Patients with a known hypersensitivity to study drugs.