In the task of Synthetic Aperture Radar (SAR) ship detection, ship targets exhibit arbitrary orientations and are closely aligned. In recent years, oriented bounding box (OBB) based detectors have gained attention as a solution to the significant overlap issue present in horizontal bounding box (HBB) based detectors. Due to the boundary discontinuity issue with current mainstream OBB methods, detectors utilizing the polar coordinate system to define OBB have been introduced. However, currently available methods are usually complicated to encode and decode, and do not take into account the complex background of SAR images. This results in the complexity of neural networks and inaccurate predictions. In this paper, we propose a novel five-parameter polar coordinate dense regression detector (FPDDet) that only uses a centroid, a mapped polar diameter, and two polar angles to deal with the overlap problem of HBB and the boundary discontinuity problem of OBB. Meanwhile, we introduce a dense regression strategy based on covariance-adaptive rotated Gaussian heatmap to dynamically assign ship target samples in response to large-scale variation of ship targets in SAR images, and we suggest a dense regression heatmap loss function to better match our dense regression strategy. In addition, we design a feature enhancement module to enhance the target features while weakening the background interference, aiming to cope with the severe noise pollution of SAR images. Experimental results show that our FPDDet achieves the state-of-the-art performance on Rotating SAR Ship Detection Dataset (RSSDD) and Rotated Ship Detection Dataset (RSDD). Compared to previous best results, mAP has been improved by 1.2% and 1.71%, respectively.