Haha..not sure I can give you the proper answer, but I'll give it a go....
Firstly of course, it is just not sensible to have two correct answers to a mathematical problem,* so there has to be a rule of convention which everyone uses.
Basically, multiplication is just a shorthand (lazy) way to express repeated addition, so you are just adding the same number together several times.
If written out in full then 5 plus 3 'lots of' zero would then be 5+0+0+0, which of course equals 5.
A couple of examples using slightly different numbers, if a fish costs 5p & chips cost 2p, then some-one ordering a fish & 3 portions of chips can be represented as
5+3x2.
If just worked out from left to right, you would be charged 5p + 3p and then it would be multiplied by 2, which would be 16p when in reality you should just be paying 6p for your chips plus 5p which is 11p.
Obviously the problem could be slightly different, for example, if apples and oranges both cost 2p each and you bought 5 apples and 3 oranges, you could also write it as 5+3x2, but in this case you would need to total first and then multiply by 2 so you need to show the need to find the total first by using brackets, (5+3)x2 to give the correct answer, which this time will be 16.
I'll stop now before I tie myself up in knots, but hope this helps a little.
(* yes, I know about roots but there's always an exception.

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