I would suggest that rather than covering many places you just go to one place and explore. These are the places you can go to-
Vizag Bon voyage!
Hi Tom, you can head to Yercaud, Chikmagalur, Hogenakkal waterfalls or do the Tamil golden triangle Madurai-Ramehswaram-Kanyakumari. Three days would be enough do cover these places. Also i'm sending with this message a post to you which will help you decide the places to visit. https://www.tripoto.com/trip/hill-stations-in-tamil-nadu
I don't know if you meant 5000/night or 5000 in total for the whole trip. But what so ever the case be would suggest you to explore local places & delicacies. Because you'd be traveling with your friends stay in a hostel type setting, this would save you a lot of money and you would get the authentic taste of the place that you are visiting.
Good Luck for your trip :)
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