To solve this exponential equation, we first simplify it by subtracting 6^x from both sides:

5^x - 6^x = 4

Now, we can rewrite the equation using the properties of exponents:

(5^x)/(6^x) = 4

Next, we can rewrite the equation using the property of exponents that states a^(m-n) = a^m / a^n:

(5/6)^x = 4

Now, we take the logarithm of both sides to solve for x:

log((5/6)^x) = log(4)

Using the power rule of logarithms, we can bring down the x as a coefficient:

x * log(5/6) = log(4)

Now, we isolate x by dividing both sides by log(5/6):

x = log(4) / log(5/6)

Therefore, x is equal to log(4) divided by log(5/6).