Image texture analysis is a dynamic area of research in computer vision and image processing, with applications ranging from medical image analysis to image segmentation to content-based image retrieval and beyond. "Quinary encoding on mesh patterns (MeQryEP)" is a new approach to extracting texture features for indexing and retrieval of biomedical images, which is implemented in this work. An extension of the previous study, this research investigates the use of local quinary patterns (LQP) on mesh patterns in three different orientations. To encode the gray scale relationship between the central pixel and its surrounding neighbors in a two-dimensional (2D) local region of an image, binary and nonbinary coding, such as local binary patterns (LBP), local ternary patterns (LTP), and LQP, are used, while the proposed strategy uses three selected directions of mesh patterns to encode the gray scale relationship between the surrounding neighbors for a given center pixel in a 2D image. An innovative aspect of the proposed method is that it makes use of mesh image structure quinary pattern features to encode additional spatial structure information, resulting in better retrieval. On three different kinds of benchmark biomedical data sets, analyses have been completed to assess the viability of MeQryEP. LIDC-IDRI-CT and VIA/I-ELCAP-CT are the lung image databases based on computed tomography (CT), while OASIS-MRI is a brain database based on magnetic resonance imaging (MRI). This method outperforms state-of-the-art texture extraction methods, such as LBP, LQEP, LTP, LMeP, LMeTerP, DLTerQEP, LQEQryP, and so on in terms of average retrieval precision (ARP) and average retrieval rate (ARR).