To solve this equation, we can use the properties of logarithms.

Given equation: Log(2, x)log(2, x)+5log(3, x)log(4, x)+ log(5,x)log(5,x)=0

Let's denote log(2, x) as a, log(3, x) as b, and log(5, x) as c.

So the equation becomes: a^2 + 5ab + c^2 = 0

Now, we need to find values of a, b, and c that satisfy this equation.

Since the equation doesn't involve x directly, we can't find x directly. However, we can find the values of a, b, and c that satisfy the equation.

Let's try some possible values of a, b, and c:

Let a = 0, b = 0, c = 0:
This gives us 0^2 + 500 + 0^2 = 0, which is true.

So one possible solution is a = 0, b = 0, c = 0.

There could be other values of a, b, and c that satisfy the equation as well.