Does time really fly when you're having fun or is that just another senseless saying?

One thing that I tried as I might but couldn't find the solve. The problem is Twin Paradox. According to the theory of relativity, as u approach the speed of light time slows down. So let's consider two twin brother. One is gonna stay on earth, n other's gonna travel a 20light years straight path by a very high speedy rocket. Now consider we measure the time that he took to finish his journey is 25years. so according to the bro who is on earth would measure that his twin completes the journey taking 25years time to reach 20LY. But he would notice that the other bro who is in the rocket, his time is running slowly, so suppose the 1st brother thinks that when his brother completes his journey it will take 5years for him to reach there. Now if we asked the 2nd brother he will say, "yes, it took 5years for me n not 25years to reach there, cz the length had shortened." so it means that the two brothers conclusion/results r the same although their definition r radically different. Now consider the 2nd brother is returning to earth with the same speed. so according to him it will take 5+5=10years to return to the earth. But according to the 1st brother, it took 50years. now my question to u guys that I couldn't find, according to relativity, the brother in the rocket would never know whether his rocket is moving. He would think that he is standing still n it is the rest of the universe which is moving. so in his perspective, time on his ship is flowing normally, n time on universe is running slower. so to him, time on earth is passing slowly. So hee would expect that when he will return to earth his brother on earth would be younger. n he would be older. But reality is the opposite. When he returns, he would notice that his brother on earth is older n he is younger. But according to relativity, both should agree on the result but their definition would be different. So to 1st brother, his brother is younger cz when he was in ship his time was passing slowly. The 2nd brother would be agree with the result, but what will be his Definition? What would happen to him that he would know that when he returns to the earth he would bee younger, not his brother on earth? n why?

ANSWERS:
1.Relativity and the Twin Paradox I The Great Courses

Extra..Proves

2.Easy to understand animation explaining all of Einstein's Theory. Covers both Special Relativity and General Relativity.(Huge and DEEP OVERVIEW)