To address the high redundancy and weak security inherent in satellite image transmission, this paper proposes an image encryption algorithm founded on a novel five-dimensional fractional-order cosine memristive Hopfield neural network (5D-FOCMHNN). The constructed hyperchaotic system exhibits long-term memory and multistability, capable of generating reconfigurable multi-scroll attractors. A multivariate bit-level scrambling strategy effectively disrupts pixel correlations using neuron state sequences. Furthermore, the system’s chaotic output dynamically governs DNA encoding rules, while a bidirectional diffusion mechanism ensures strong randomization and resistance to differential attacks. Comprehensive experiments demonstrate that the 5D-FOCMHNN-based scheme provides a key space of $2^{256}$, has an information entropy approaching the ideal value of 8, and exhibits robust resilience against cropping, noise, and statistical cryptanalysis, thereby providing a highly secure solution for satellite image transmission.