My first response is: Why the nut do they have a weight limit on basketball players? Don't they know that taller guys weigh more and are better at the sport?
Anyway, I really wouldn't be recommending that you lose more than 1-2kg/month, so to get from 95kg to 90kg, you'd be looking at 3-6 months. Probably not what you wanted to hear, but it's highly impractical to lose weight more rapidly than that, and as a teenager, you need to eat.
In saying that, your body weight will probably fluctuate by about 2kg per day based on how much food and water is in your system. If you haven't eaten or drank anything, and you have expelled your bowels before weigh-in, you'll have a lower scale-weight than if you're freshly stuffed, so you might be able to lose 3kg of body fat over the next 6-12 weeks, and get by on being hungry and thirsty on the day you weigh in. In saying that, use your brains. Getting on the team means nothing if you topple over from hunger or dehydration. Health comes first.
As far as exercise goes, just play basketball/run drills if it's safe to do so. Do you have a basketball hoop in your backyard (do you have a backyard?)?
As far as nutrition goes, focus on getting a healthy balance of foods first: meat, vegetables, fruit, milk, nuts, legumes, whole grains...reduce processed foods and added fat/sugar. Then assess how your weight is changing (if at all) after a few weeks. Modify either the size of each portion, or the number of portions you have (depending on what you find easier to adhere to -- if you've got 6 good meals a day, some people will find it easier and more comfortable to reduce the size of each portion by 10%, others will find it easier and more comfortable to maintain portion size but only have 5 meals a day), until you're losing 1-2kg per month as I recommended above.