0
undefined means you can not do the operation (5/0 is undefined)
no solution refers to an equation not having an answer.
a solution is a number which you can plug into the variable of an equation and get a true statement. So having no solution means there is no number which you can plug in and get a true statement.
As a fraction is not an equation, but an expression it is not right to say that 5/0 has no solution. There is no variable in 5/0, nothing to plug into to get a true or false statement.
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