Evaluate the expression $a^3\cdot a^2$ if $a= 5$.
To evaluate this expression, I need to apply the rules of exponents and arithmetic. I recall that $a^3\cdot a^2 = a^{3+2} = a^5$, by the rule of adding exponents when multiplying powers with the same base. So, I can rewrite the expression as $a^5$, where $a= 5$. Now, I just need to compute $5^5$. I can do this by multiplying 5 by itself five times, or by using a calculator. I get $5^5 = 3125$. 