Of course 10w-30 is much better, and another recommended engine oil grade, than that 5w-50.
A similar chart is also there on https://shell.pakwheels.com/generic-recommender , but it can not be followed blindly.
Most recommend to switch to thick engine oil grades, when vehicle is high on odo / high on age (whichever comes first), but its just speculation.
If an engine, let's say 2NZ-FE in PKDM Toyota Corolla requires 5w-30 / 10w-30 (Source: http://mywikimotors.com/toyota-2nz/ ), the car is brand new, you start pouring 5w-30 since day 01, the oil is preferably fully synthetic, from some reputed brand, and original, you change oil and filter after regular, OEM recommended drain intervals; then even if you drive for 2 lac + Kms, it will not require switching to thick oil (unless / until engine had been severely abused).