In the Binomial Theorem, the general term in the expansion of \((a + b)^n\) is given by:
\[ T_k = \binom{n}{k} a^{n-k} b^k \]
In this case, we have \(a = 3x\), \(b = -5y\), and \(n = 5\). The last term in the expansion corresponds to \(k = n\).
For the given expression \((3x - 5y)^5\), the last term is when \(k = 5\):
\[ T_5 = \binom{5}{5} (3x)^{5-5} (-5y)^5 \]
Calculating this:
\[ T_5 = \binom{5}{5} (3x)^0 (-5y)^5 \]
\(\binom{5}{5} = 1\) and \((3x)^0 = 1\), thus:
\[ T_5 = 1 \cdot 1 \cdot (-5y)^5 = (-5y)^5 \]
Now, we calculate \((-5y)^5\):
\[ (-5y)^5 = -5^5 y^5 = -3125y^5 \]
Therefore, the last term in the expansion of \((3x - 5y)^5\) is:
\[ \boxed{-3125y^5} \]