There is a subtle difference in meaning between these two expressions when you are listing items.
This company promotes employees from within like Tom, Dick, and Harry.
This company promotes employees from within such as Tom, Dick, and Harry.
In the first sentence, Tom, Dick, and Harry are not necessarily the people being promoted from within; rather, people from within who have characteristics similar to them, or people like them, are being promoted.
In the second sentence, Tom, Dick, and Harry are cited as examples of people from within who have been promoted.
Here’s another set of examples:
PetroAir plans to have direct flights to major oil industry centers like Dubai, Aberdeen, and Houston.
PetroAir plans to have direct flights to major oil industry centers such as Dubai, Aberdeen, and Houston.
Although this sentence could go either way, the first example hints that other cities with a critical mass of oil professionals would likely have direct flights, whereas the second example gives three cities that are certainly on their list. Subtle, but different.
In short, if you mean “resembling,” use “like,” and if you are citing specific examples in a group, use “such as.”