You may never know for sure, but production started in '36 and all pre-war examples came with checkered stocks which may help unless the stock is not original. Savage did use date codes on other rifles before serial numbering came about, which was after the Model 5 ceased production, any other markings?
A=49, B=50, C=51, D=52, E=53, F=54, G=55, H=56, I=57, J=58, K=59, L=60
M=61, N=62, P=63, R=64, S=65, T=66, U=67, V=68, (W=69, X=70)