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x=x+5 is not an equation as the answer to this is not possible. The values of X should be same and not different.
On the other hand, x=1 is also not an equation, it is the answer of the equation.
An equation has coefficientc variable, operator and constants where the sum of left hand side of equation and right hand side is equal. For example 3y+5 =23is an equation with value of y as 8.