Let's solve this problem using the properties of logarithms. We are given that log 10 to base 8 = X, which can be written as:

8^X = 10

We want to evaluate log 5 to base 8 in terms of X. Let's call this value Y, so we have:

8^Y = 5

Now, we can use the fact that 10 = 2 * 5 to rewrite the first equation as:

8^X = 2 * 5

Taking the logarithm of both sides with base 8, we get:

log (2 * 5) to base 8 = X

Using the logarithmic property that log (a * b) = log a + log b, we can rewrite this as:

log 2 to base 8 + log 5 to base 8 = X

Substituting Y for log 5 to base 8, we get:

log 2 to base 8 + Y = X

Y = X - log 2 to base 8

Since log a to base b = 1 / log b to base a, we can rewrite log 2 to base 8 as:

log 2 to base 8 = \(\frac{1}{\log_{2}8}\) = \(\frac{1}{3}\)

Substituting this value into our equation for Y, we get:

Y = X - \(\frac{1}{3}\)