I have an employer sponsored account(401k by Fidelity) which was opened in my first company. Now I am in another company. To reduce my tax liability, can I add $5000 to the account so the amount is tax deductible?
You cannot contribute directly to that 401k account if you no longer work at the sponsoring company - you have to be on their payroll.
You can, however, roll the 401k over into an IRA, and contribute to the IRA. Note that in both cases, you are only allowed to contribute from earned income (which includes all the taxable income and wages you get from working or from running your own business). As long as you are employed (and have made more than $5k this year) you should have no problem.
I am not certain whether contributing your $5k to a roth IRA would help you achieve your tax goals, someone else here certainly can advise.