To solve the equation [16^x] - 6*[4^x] + 5 = 0, we can rewrite it using the properties of exponents.

Let's start by expressing 16 and 4 as powers of 2:
16 = 2^4
4 = 2^2

Substitute these values into the equation:
[2^(4x)] - 6*[2^(2x)] + 5 = 0

Next, use the properties of exponents when raising a power to another power:
2^(4x) - 6*2^(2x) + 5 = 0

Let's simplify the equation:

Let y = 2^x, y^2 = 2^(2x), y^4 = 2^(4x)

Now, our equation becomes:
y^4 - 6y^2 + 5 = 0

This can be factored as:
(y^2 - 5)(y^2 - 1) = 0

So, y^2 = 5 or y^2 = 1

This results in two cases:

1) y^2 = 5:
y = ±√5
2^x = ±√5
x = log2(√5) or x = log2(-√5) - Note: This case is not valid, as the logarithm of a negative number is not defined for real numbers.

2) y^2 = 1:
y = ±1
2^x = ±1
x = 0 or x = log2(-1) - Note: This case is not valid as well, as the logarithm of a negative number is not defined for real numbers.

Therefore, the only valid solution is x = log2(√5).