To find the number of students who support the new school administration among the 1,500 students surveyed, we can set up a proportion based on the ratio of students who support the administration.
Given that 5 out of every 8 students support the new administration, we can calculate the number of supporters as follows:
\[ \text{Number of supporters} = \left(\frac{5}{8}\right) \times 1500 \]
Now, performing the multiplication:
\[ \text{Number of supporters} = \frac{5 \times 1500}{8} = \frac{7500}{8} = 937.5 \]
Since the number of students must be a whole number, we round 937.5 to the nearest whole number, which gives us 938.
Thus, the most reasonable number of students among the 1,500 surveyed who support the new administration is
\(\boxed{938}\).
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