Yes, it can be solved quite easily without a calculator. Let's do it step by step.

$log_5(20) + log_5(10) - 3log_5(2) = log_5(20) + log_5(10) - log_5(2^3) = log_5\left(\dfrac{20 * 10}{2^3}\right) =$

$log_5\left(\dfrac{200}{8}\right) = log_5(25) = log_5(5^2) = 2log_5(5) = 2 * 1 = 2.$