I live in an apartment that is owned by a large university so I don't think they monitor electricity usage or anything like that.
Also, how long does it take to set up the mining equipment? I have little knowledge about computer systems and mining equipments. and I would like to mine to earn bitcoins and learn about them at the same time.
Obviously you could inquire of your landlord regarding the electrical capacity for your apartment. My bet is that is when they will make clear your terms of usage, and I'll bet that a "money making enterprise", such as Bitcoin mining is prohibited.
If you want to "fly under the radar" your electrical capacity will run out long before your $5000 budget does in terms of mining hardware. While your electricity appears low cost, or nearly free, it isn't. If you get cross-wise with the University over electrical usage, you could have much bigger problems with your education, than just Bitcoin mining. I think learning is fine, but maxing out your electrical usage and budget won't bring you any great riches.
One last item. What if 20% or more of the other students in your housing complex followed your lead? Do you think the University still wouldn't notice? Do you think they would condone and/or ignore you running a long extension cored out the window and selling recharges for Plug-in electric car?
Just my $.02.