These two verses belong together. Proverbs 25:4 provides the image, whereas Proverbs 25:5 gives the application of it. It has value to first let the image penetrate your mind.
With silver, one is to work diligently and skillfully. This takes a lot of effort from the silversmith. Silver naturally contains a lot of impurities, which need to be entirely removed first. But after that is done, one can craft something beautiful that someone can enjoy.
It is similar when wicked individuals are being dealt with resolutely. Then they cannot execute their evil plans. They have been rendered harmless. Through it all, the throne of the king is again secured. Right away, it creates space for a just government that benefits all subjects. Justice takes its course. Society can flourish once again. It is beautiful when all this takes place.
This remains current, also for today. We live in a world where evil has nestled itself in the hair follicles of society. No man is pure anymore. We are inclined to do evil, often much quicker than we think. Therefore, we all need to be tuned up. That is especially true when we have great responsibilities regarding the government of a country or an organization. We can learn this specifically from these combined verses.
Right away it becomes clear how beneficial it is when those who are wicked are removed.
The result of this can be compared to a beautiful silver bowl, which glitters gracefully in the sun.
4 Take away the dross from the silver, and the smith has material for a vessel;