Raman travels 5 km south, turns right and walks 3 km, then turns left and walks 5 km. In which direction is he now from the starting place?

The final position lies to the south-west of the start.

Take the start as origin and track each leg.

5 km south reaches (0,-5).

A right turn faces west; 3 km gives (-3,-5).

A left turn faces south; 5 km gives (-3,-10).

Negative x (west) with negative y (south) means south-west.