Ok, so I have a tier 4 scout, and its next upgrade takes like 5,000 EXP to research. So what would be the easiest way to earn that much EXP in a short amount of time?
Damage dealt is the primary source of xp, damage dealt to higher tier tanks even more so. If you can damage enemy tanks, especially high tier enemies, you'll get xp. If you can't damage enemies, the next best bet, especially in a tier four light is to assist allies in doing damage. The two ways to do this and get credit are to track enemies that receive damage while tracked by you, or to spot enemies that allies who otherwise wouldn't be able to see shoot while lit by you. Working in coordination with your teammates is essential for getting assistance credit for the damage they do, but by lighting enemies you can get significant xp.
Another option is to take a path that doesn't go through a tier four light, because if the matchmaking for them is as bad as in the PC version, it's often easier to not go up against so many high tier tanks (tier fours got matchmade as dedicated scouts in higher tier matches).
Other than focusing on xp generation, another very important thing for playing well and maximizing xp gain is to know when a risk is worth it and when you should really be preserving your hp. Health is a resource to manage, and light tanks can do considerably better in the later game, when enemies are alone.
XP accumulates on individual tanks quickly, and in the free XP pool slowly. Free XP can be used on ANY tank regardless of type or nation. The only time tank XP can be used for other tanks is if you've already elited your tank and haven't been spending it on the crew, but this doesn't matter if you're still chasing unlocks.
Play the game in the tank you want to upgrade first and foremost.
If you die before the round ends, your next choice of tank should be the tank which gives you the most amount of free XP - high tier, premium and something that hasn't used it's daily double will help.
HOWEVER - in such situations you can end up starting a round in a different tank to fill the time, and find the round where your desired tank is stuck ends not long after you start, meaning you're slaving away for maybe 20-50 free XP while you could be earning 400-1000 XP on your chosen tank in that time. For that reason, tanks which favour quick rounds are preferable. Generally dieing early so you can finish a round is bad play, however the right YOLO tank can still allow you to do this while helping your team.
Do more damage, xp gained is proportional to that.
For a scout, do more 'scouting assisted' damage - where your team shoots tanks that they wouldn't see themselves, but are spotted by you.
Die less, as you need to focus your earned xp to that particular tank, so you need to be doing damage in it instead of sitting in garage waiting for the next game.
And, of course, 5k is a tiny amount of xp - you'll get to 100k xp costs rather soon.
As @SysDragon says, play a lot. And be sure to play a lot with vehicles of that same nation and tier, as exp doesn't translate across nations and tiers (though you can invest real $$$ and buy gold which allows you to do that).
There's no other way apart maybe from investing real $$$ and buying exp (wouldn't surprise me if that's an option in the online store, the game is pay to win after all).