I have had five prior UK visa refusals, should I still apply for UK tourist visa?

Normally we need to see a scan of the refusal notice, but five of them obviates that requirement. Your situation has moved on from a "plain vanilla" refusal.

An unbroken sequence of five refusals indicates that you are in a 'serial refusals' tailspin. Part of this situation means that they are no longer able to consider applications on their merit because the history has taken on a life of its own. I.e., that your fixation on getting to the UK has convinced them that you are not a genuine applicant. Or to put it more bluntly, genuine applicants will either resolve the issues on the second or third attempt or they will find some other place to visit and move on with their life.

You need to start being a little bit careful because if they get the idea that your applications are frivolous, they can issue a ban (Paragraph 320, subparagraph 11 (iv) "...making frivolous applications..."). It's their recourse against people who appear to be obsessed or in some other way 'disturbed'. We had one of those here a few weeks ago demonstrating that bans are accumulated consecutively rather than concurrently. So be thinking about that factor before jumping in again.

I am planning to apply once again and want to go for a 2-week visit.

Why? The cure for serial refusals from the UK is invariably to build up a track record of performance in the affluent Commonwealth (Canada, Australia, NZ and so on) along with other non-Commonwealth countries like the USA, Japan, and Ireland. Schengen experience can be helpful also.

I do not have the previous refusal letters; how would I get those?

You can submit a Subject Access Request by writing to the Home Office at 2 Marsham St, London SW1P 4DF, United Kingdom. The Information Commissioner has thoughtfully provided a sample template on his site (an MS Word Document). Usually they will not release the refusal notices themselves (at least in my experience) because it's not in the public interest, but will provide an extract or summary (if they honour the request in the first instance).

Should I apply for the UK tourist visa or not?

It's a matter of opinion. What is not a matter of opinion is that you need representation by a member of the Law Society, and they won't even think about it without seeing your refusal history. Since you do not have those and are about a year away from getting anything, it doesn't make a lot of sense does it?

I cannot apply for any other country.

This is wrong. A lot of people with refusal histories think they need to 'clear their name' before they can move on with their life. But there is nothing preventing your filing an application to Thailand, Russia, Vietnam, Kazakhstan, and other countries in that area. Peripatetic history of any sort is always helpful.

NOTE: I assume you are South Asian and your currency is denominated locally. More to the point, those things do not matter in this case.

First, the reason for your visit may not be clear this time. The first one was a group visa with cricket members, but this time it's individual visa. They may believe that you are not going to return back if granted a visa.

Secondly, you have been in the UK twice before, so there is no reason to keep applying to come back. Instead, try applying for other countries and give it time before making another application.

In your application what is the purpose of visit (tourist, visiting family or relatives, friends)? What makes you want to return to visit and where in UK (London, Manchester, Scotland etc.)? How long is your stay (2 weeks, months)? Also, why UK and not anywhere else?