Question 32108
Well, this is not any kind of equation.  It is, however, an expression, so the answer to your question is ...no, it is not a Diophantine equation!

But perhaps you meant to write:
5x + 6y = 27

If this is the case, then the answer is yes.

This would be an example of a linear Diophantine equation of the form: ax + by = c

In general, linear Diophantine equations are solvable iff c is divisible by the greatest common divisor of a and b. By "solvable" we mean that there exist integers, x and y, such that ax + by = c