The mean of her first five quiz scores is found by adding the scores together and dividing by 5:
(84+72+90+95+87)/5 = 428/5 = 85.6
Any value higher than this mean for the sixth quiz score will raise the overall mean; any value below this mean for the sixth quiz score will lower the overall mean. This means the values that could increase her mean are 90, 86, 92 and 89.