If I purchased $5000 in stocks for one company (on NASDAQ), will that be counted as an investment expense thus reducing the amount of taxable income that I have for the year?
Assuming you are in the US, and are an average joe, the answer to your question is no. Investment costs do not reduce your taxable income for the year you make the investment. They do factor in to the cost basis of your investment and so will affect your taxes in the year you sell the investment.
If you want to reduce your taxable income, you could contribute the $5000 to a traditional ira, or 401k, assuming you qualify. Depending on where the account is held, you may then be able to use that $5k to purchase stock in the company you are interested in. The stock would be held in your IRA or 401k account, and would be subject to more restrictions than a normal brokerage account.