The development of synthesis methods with enhanced control over the composition, size and atomic structure of High Entropy Nano-Alloys (HENA) could give rise to a new repertoire of nanomaterials with unprecedented functionalities, notably for mechanical, catalytic or hydrogen storage applications. Here, we have developed two original synthesis methods, one by a chemical route and the other by a physical one, to fabricate HENA with a size between 3 and 10 nm and a face centered cubic structure containing three (CoNiPt), four (CoNiPtCu and CoNiPtAu) or five (CoNiPtAuCu) metals close to the equiatomic composition. The key point in the proposed chemical synthesis method is to compensate the difference in reactivity of the different metal precursors by increasing the synthesis temperature using high boiling solvents. Physical syntheses were performed by pulsed laser ablation using a precise alternating deposition of the individual metals on a heated amorphous carbon substrate. Finally, we have exploited aberration-corrected transmission electron microscopy to explore the nanophase diagram of these nanostructures and reveal intrinsic thermodynamic properties of those complex nanosystems. In particular, we have shown (i) that the complete mixing of all elements can only occur close to the equiatomic composition and (ii) how the Ostwald ripening during HENA synthesis can induce size-dependent deviations from the equiatomic composition leading to the formation of large core-shell nanoparticles.