The five period moving average is calculated using the following formula:$[$Forecast for Period $8=$Period $1+$Period $2+$ Period $3+$ Period $4+$ Period$5)/5(53+48+62+68+59)/5=59][$Forecast for Period $9=($Period $2+$Period $3+$ Period $4+$ Period $5+$ Period $6)/5(48+62+68+59+50)/5=55][$Forecast for Period $10=($Period $3+$Period $4+$ Period $5+$ Period $6+$ Period $7)/5(62+68+59+50+55)/5=55]$Therefore$,$ the five period moving average forecasts for periods $8,9,$ and $10$ are $59,55,$ and $55$ respectively. The five period moving average forecasting method is a simple and straightforward way to generate forecasts for future periods based on the actual demand and forecast for the current period. The forecast for each period is calculated by taking the average of the actual demand and forecast for the previous five periods. Final answer: The five period moving average forecasts for periods $8,9,$ and $10$ are $59,55,$ and $55$ respectively.