Does the addition or multiplication rule have precedence deciding the significant figures in 5×5.364?
If this is the question in its entirety, then you should not try to 'guess' what the origin, and therefore the accuracy, of the measurement 5 is. You should take it on face value, and complete the calculation using the multiplication rule, as the equation is requiring a multiplication operation. In this case, you should have one significant figure only. 

The only ambiguity you need to consider in calculating your significant figures is whether the '5' is an exact number or not. Exact numbers come about either by definition (1 hour = 3600 seconds) or by counting (5 measurements were made) and have an infinite number of significant figures. Hence, they do not affect the accuracy of your measurements. Exact numbers are usually integers (speed of light and number of centimetres in an inch are a couple of exceptions). My guess is that your question is simply a case of going through significant figures calculations, using the information provided. To avoid ambiguity in the case of a single significant figure measurement, one could consider writing 5 as 5E0, or 5x100.

If you know 5 to be an exact number (ie the question gives that information), then you would still complete the calculation using the multiplication rule, but assume infinite number of significant figures for 5. In this case you would have 4 significant figures.