An easy proof of Ramanujan's famous congruences $p(5m+4)\equiv 0\equiv \tau (5m+5)(\mathrm{m}\mathrm{o}\mathrm{d}5)$

We present a proof of Ramanujan’s congruences $$p(5n+4)\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}5)\text{ and }\tau (5n+5)\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}5)\mathrm{.}$$ The proof only requires a limiting case of Jacobi’s triple product, a result that Ramanujan knew well, and a technique which Ramanujan used himself to compute values of $\tau (n)$.