Prostate cancer (PCa) is one of the most common newly-diagnosed types of cancer and a leading cause of cancer-related death among men worldwide. Benign prostatic hyperplasia (BPH) is another common pathology in ageing men that gradually enlarges the prostate over time, thereby producing bothersome lower urinary tract symptoms. PCa originating in larger prostates tends to exhibit more favorable pathological features, but the fundamental mechanisms that explain this interaction between BPH and PCa are largely unknown. We propose a mechanical explanation for this phenomenon: the mechanical stress fields that originate as tumors develop are known to impede their growth dynamics, and prostatic enlargement due to BPH contributes to these mechanical stress fields, hence further restraining PCa growth. To investigate this hypothesis, we run a qualitative simulation study using a mechanically-coupled phase-field model of PCa growth and leveraging a patient-specific geometric model of the prostate and tumor extracted from magnetic resonance imaging data. Our simulations rely on isogeometric analysis to accurately and efficiently handle the complex geometries of the prostate and growing tumors. Our results show that the mechanical stress accumulated in the prostate by BPH over time hinders PCa growth and limits its invasiveness. Additionally, we extended our model to explore the effect of 5-alpha reductase inhibitors (e.g., finasteride, dutasteride) on prostatic tumor growth. These drugs are commonly used to reduce the prostate volume of BPH patients, but they have also been investigated for PCa chemoprevention due to their inhibitory hormonal effect in both healthy and cancerous tissue. Depending on the relative intensity of either of these two mechanisms, our simulations show different tumor growth dynamics ranging from long-term inhibition of PCa growth to rapidly growing large tumors, which may evolve towards advanced disease. This last case would contribute to explain the controversial higher rate of advanced PCa cases found in the treatment arm of PCa chemoprevention trials of 5-alpha reductase inhibitors. In the future, we think that our computational technology can contribute to further investigate the biophysical mechanisms underlying PCa and BPH, and ultimately assist clinicians in the management of these diseases by forecasting pathological and therapeutic outcomes on an organ-scale, patient-specific basis.