Explanation:

- The speed ratio of the two trains is given as 5:8. This indicates that for every 5 units of speed the first train has, the second train has 8 units.

- The second train runs 600 km in 4 hours. To find its speed, divide the distance by time: 600 km / 4 hours = 150 km/h.

- Using the speed ratio 5:8, let the speed of the first train be $5x$ and the second train be $8x$.

- Since the second train's speed is 150 km/h, we have $8x=150$.

- Solving for $x$, we get $x=18.75$.

- Thus, the first train's speed = $5x=5\times 18.75=93.75$ km/h.

The correct answer is:

- Option 4: 93.75