With programming, it is never "random". Even the random generator uses an algorithm to predict a random number. But, if knowing the method of generation, is it possible to, let's say predict next 5 numbers that will be generated?
Yes, it is possible to predict what number a random number generator will produce next. I've seen this called cracking, breaking, or attacking the RNG. Searching for any of those terms along with "random number generator" should turn up a lot of results.
Read How We Learned to Cheat at Online Poker: A Study in Software Security for an excellent first-hand account of how a random number generator can be attacked. To summarize, the authors figured out what RNG was being used based on a faulty shuffling algorithm employed by an online poker site. They then figured out the RNG seed by sampling hands that were dealt. Once they had the algorithm and the seed, they knew exactly how the deck would be arranged after later shuffles.