The contract says financial support is for 5 years. I am not able to support my own living cost.
You need to ask someone in your department (your advisor, or whoever is in charge of the graduate program). Five years is pretty good, and it's unlikely they will guarantee more than that, but departments vary in how they handle students who outlast their funding:
Some departments simply cut people off. At that point, you have to support yourself through loans, savings, or a job (which could be an outside job or extra teaching, depending on what's available). This can be quite a burden, and it's an incentive to graduate in five years.
Some departments will offer an additional year of funding if they can afford it and think you will make good enough use of it. It's not guaranteed, but it might happen if you need it.
There may be other sources of funding, such as your advisor's grants or a dissertation completion fellowship. Whether this is feasible depends heavily on the field and your personal circumstances.
There's no generic answer, and nobody on the internet can tell you which of these cases might apply to you.
The only correct answer is "possibly."
If your contract says 5 years, that means they're only promising you 5 years. Beyond that, they are within their rights to refuse to offer extra funding.
Depending on how well-funded your advisor is and whether he/she believes you're making acceptable progress, it may be possible for him/her to fund you beyond 5 years.
This very much depends on your institution and your professor.
In some institutions (particularly many European ones), there is a very strong expectation that you will finish and get out in the time allotted, and you may well lose all funding.
In others, it means that after the guaranteed period, it will be up to you and your professor. This was the culture where I did my Ph.D. My funding was only guaranteed for two years, if I remember correctly, but I actually spent seven years as a graduate student, and that was a fairly typical length in our department. As time went on, I got more involved in securing my own funding, eventually becoming the primary writer on a couple of funded NSF grants (though not the PI, given that I was just a grad student).
You can try to find out which is the case by asking people at the institution. In either case, however, I would recommend against worrying about it in the beginning of a Ph.D., particularly with a nice long five-year guarantee to work with: a healthy department and good advisor with either type of culture will help to steer you to an appropriate path to graduation, and five years is quite a long time.
Just to share an Australian perspective: A PhD scholarship is typically three years full-time. After that, traditionally there was an easy-to-get extra 6 months of scholarship (although this may be getting harder to get with increased pressure being put on timely completion). After that (i.e., 3 years and 6 months) getting a further 6 months scholarship is rare. At the university level it would typically require exceptional circumstances. Alternatively, occasionally supervisors will have additional money to pay the scholarship for an additional period.
More generally, when PhD students go beyond the scholarship period and need money, they combine work with finishing their PhD. Naturally, there are a whole range of ways that this is done. Generally, by the time you reach this phase of your PhD, you will have a range of marketable skills. In some cases your supervisor, department, or university may have teaching or research roles that are suited to part-time or even full-time work.
The challenge is to keep the money flowing while at the same time getting enough sustained thinking time to finish the thesis. I've known a few people at this stage who stopped working completely in order to get a solid few months of thinking and writing time to finish the thesis. I've also known others at this point who never finish their PhD because full time work takes over and they never find the time to dedicate to finishing the thesis.
Usually this means that you will lose funding from the University. However, there are always professors with grant money.
You should spend your first few years networking and finding a professor with funding and research interests similar to yours and then try to get them to hire you as their research assistant.
I also know someone who took 9 years to get a PhD because he was able to work as an instructor and get funding from a different budget from the one they have to fund TAs.
In other words, if the department wants to keep you around for longer since your research looks promising but needs more than 5 years, they will help you find the funding. If it looks like your research isn't going anywhere, stopping your funding is a way to gently nudge you out.
I'm about to enter into my fifth year (next fall). However, I entered my program with just a BA, so I had to get my MA with thesis en-route to the PhD. I also had to take 4 years of classes. I will be proposing my dissertation at the start of next Fall. There's definitely pressure to finish, as in you get the gentle tap on the shoulder that it's your time to graduate. I'm excited about it. However, rarely have I seen a student, even who entered with an MA, finish in 5. I've never seen a student loose funding. In my department there is no shortage of TAships to be had if your advisor is in between grants- though there is no guarantee of funding.
I don't know if I'm the only one to notice this, but it almost seems like when the department/labs are flowing with money students finish much slower. When money is good I've seen a year or two added to students' timelines some what arbitrarily under the auspice that "It takes the time it takes to get a PhD." Whereas, when money is tight students fly out of the department. Maybe standards for dissertations drop to get people out the door? I'd like to think that doesn't happen, but I often wonder if keeping highly-skilled cheap labor around to do something with the data that a PI is collecting from a high-profile grant is often an implicit factor that impacts students' trajectories. In which case it is not uncommon to see students in their 6th or 7th year of the program receive funding.
Disclaimer: I never did a PhD, however I was a staffer so take this with a grain of salt. The university does not want you to fail. its got a lot of money and resources invested in you, especially so with your supervisor. Theres two competing forces at play here. The first is the universitys incentive for you to succeed. This can be things like patents, marketability of successful research, continued funding, and of course prestige. On the other hand universities are somewhat resource constrained entities, you need to balance against this triage of resources. If the risk outweighs the benefits of continuing funding its not going to look good. Whether this is determined per case or via policy will depend on your institution, but whats important is you make a CASE for yourself and why you research is worth their money. Whatever the case is, you need allies in your department, starting with your supervisor and going up the chain. Get them excited for you.
Just to share my anecdote. (I am at some particular department of some particular US university.)
I am now in my 6th year. My offer letter promised me only funding for the first four years (fellowship for the first year, teaching assistant for the next three).
Nonetheless I was able to get funding for my 5th and 6th years. In my case as a teaching assistant. Sometimes people do end up getting no funding for some semesters or years, but typically even in that case they get a tuition waiver.
I cannot be sure but my experience at this particular department of this particular US university is probably typical at US universities.