There is no way that a La-5FN should be able to catch a P-51D if both are flying in a straight line. At lower altitudes I would probably use a shallow dive just to be sure as the La-5FN is quite good down in the thicker air... but get up to the higher altitudes and the Mustang walks away from nearly every Russian bird.
Quoting the top speeds of the La-5FN and P-51D doesn't mean a whole lot... what altitude were you at at the time. The top speeds of many aircraft are very important depending on what altitude you're working with. It's not like the P-51 gets 437mph top speed at every single altitude if flies at.
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