How do I win against legendary decks?

First, a few points about your question. Rank 25-20 is very easy. I would not give much credence to your performance in those ranks. Second, losing 5 games in a row could just as easily be bad luck. What matters is your performance in the long run.

Most legendaries alone will not swing a game, or simply require dumb luck to do so. There are also a relatively limited pool of legendaries that you'll come across. Learn what those are. Here's how I deal with them:

Save removal

Save your counters and other cards as best you can. Playing against a secret paladin? Save your counters for the very likely Tirion. They are probably holding on to him waiting for you to burn your removal cards.

Ignore it

If you can gain tempo early and maintain board control, there's a very good chance that by the time your opponent plays a legendary it will be too little, too late. Most of the time if your opponent plays a legendary and you lose, there's a good chance you were already losing anyway. Outside of some really good luck (a lucky Ragnaros hit) most legendaries aren't enough to immediately swing a game.

Win before it's a problem

Most legendaries are high cost cards. Focus on decks that will let you win before they even get a chance to play them, such as variations of Zoo decks that focus on lots of low cost minions. This ties into my previous point, gain tempo and board control early.

Conclusion

It's entirely possible you'll lose a game due to a crucial legendary card from your opponent and there was absolutely nothing you could have done to avoid it. It'll happen. A single game means nothing aside from tournaments. Focus on your play and strategy. Legendaries are powerful, but they alone can not win a game. More often it was not the legendary you lost to, but the other cards and good plays that aren't as flashy. You just remember the legendary.

• Keep your hard removal for their big creatures that are hard to remove for you.
• Learn the popular decks to know what to expect from them.
• Try to adapt some of the popular deck that you have already most of the cards.

That's about all I can think of. Basically the main point is that you should be smarter than them.

Some of the smarter decks to go with low dust cost would be Zoo and Face Hunter (Yes you can hate me for saying this). These decks really cost next to nothing in dust cost and are extremely annoying to deal with.

P.S. Be aware that there will be a rotation of cards in standard, so stay away from Goblins vs Gnomes and Naxxramas since they won't be available in this mode in May.

If your collection is small and you're trying to compete, I would focus on the Win Before Its a Problem strategy. Complete answer:

Work towards making a simple, cheap deck that plays quickly. You'll get more games and experience under your belt, and you can actually win against any deck no matter how strong it is because you blow them up by turn 5 - 7 with a good start.

The least expensive option is Face Hunter which you can find here . From that deck list, sub out the Leeroy for any charge minion and it will still be very effective. The deck as listed contains basic, common, and a few rare cards so it's very approachable.

Other decks you could look into are Warlock Zoo, Shaman Aggro, Tempo Mage, Aggro Paladin, or Egg Druid. Each of those is more costly than Face Hunter (except maybe Aggro Paladin), but if you're only playing one deck over and over you should probably enjoy the idea of it and have some fun too.

As some of the other answers already say, legendary cards will not automatically win a game. Yes, they're powerful, but very few of them will turn the tide instantly from one person to the other. Likely, the real issue is you are coming up against people who have better deck synergy than you do because they have many more cards in their library, as evidenced by their number of legendaries. This is the real blocking point for many new Hearthstone players.

To counter this lack in your own library, the number one thing you need to focus on is defeating the various solo adventures. Some of the best cards in the game come from there, like Loatheb or Kel'Thuzad, both legendary as are many of the other rewards. Until you can manage to increase the size of your library, you need to focus on building decks that don't require specific cards to perform well. For many people, this means Zoo warlock decks and basic mages. You need 0 cards outside of the basics to perform well as a mage because they get board clears, removals, etc all as part of their level up line. Warlocks often have a card advantage due to their hero power so they play well with lots of small minions that can zerg the other player if they don't get their board clears early on.

As was mentioned, 5 losses straight doesn't mean much when you're new. Its a fun game that becomes more fun when you can actually compete more fairly. Until then, focus on the weaknesses of the game, like the imbalance that the Mage class has, and go from there.

Also, play tavern brawl every single week. Your first win gets you a free card pack and you can complete quests there. And many weeks, you are playing with decks that are created randomly or given to you and don't require that you have the cards yourself. Brawls are a great way to learn the intricacies of the meta game, even though many of them heavy favor mages.

First I want to note that you should get used to losing streaks. It's just a nature of the game, sometimes it goes like that and 5 losses in a row is mild, you got worse ahead. :)

As for legendary advantage it's not quite simple as that.

At any point in time there are subjectively (and borderline objectively) top tier decks — those that are incredibly polished engines of destruction, made from cards available at the time.

Below them are the rest of the decks either less strong or purposely made to target top tier decks (welcome to metagame).

Since you are new player and by definition don't have elaborate card collection yet — your deck building options are very limited.

If you want to progress higher in ranking here are the things that you should focus on:

1. Improve your collection. No getting around it. Research how to optimize gaining gold, consider if Arena is interesting for you to aim for prizes there, decide which legendaries you might want to save dust to craft.
2. Improve your skill. At the moment you are winning against players of similar skill, playing decks of similar power. Getting stronger as a player gets you to the point where you can win against people with stronger decks, who are playing them less well.
3. Find and make strongest deck you can afford. While many of strong decks contain multiple legendaries, not all of them do. Some deck archetypes are historically affordable. For example as long as I've been playing Warlock Aggro Zoo has been balancing between affordability and power. It was first deck I played in ranked a lot.