To solve this equation, we need to apply the properties of logarithms.

We know that 5^log5x = x^4
We can rewrite this as 5^log5x = 5^(4log5x)

Now we set the exponents equal to each other:
log5x = 4log5x

Divide both sides by log5x:
1 = 4

Since the equation is not true, there seems to be an error in the original problem. Let's reevaluate the equation:

Given: 5^logx5 = x^4

Using the property that a^loga^b = b, we can rewrite the equation as:
logx5 = 4

Therefore, x = 5^4 = 625

So, the correct solution to the equation 5^logx5 = x^4 is x = 625.