Using a weighted moving average forecast with a weight of $0\mathrm{.}5$ for the most recent period, $0\mathrm{.}4$ for the next most recent, and $0\mathrm{.}1$ for the next, a forecast of $57$ was computed for period $7.$ If the demand for period $6$ was $54$ and the demand for period $4$ was $60,$ what was the demand for period $5?$