Just to confirm, the other party was a learner (only held a provisional license), yet was driving alone - which is clearly against the law.
Also they were driving "on some one else insurance"? I don't even know what that means. Insurance covers the policyholder and one or more named drivers (often family members). Are you saying that he wasn't the policyholder, by was specifically named on the policy - i.e. a named driver?
The we get to "in car he just bought". So he owns the car, but someone
else is the insurance policyholder? Is that what you're saying? Who is the policyholder? One of his parents, perhaps?
By "After 5 days my company cannot speak to any one", do you mean that your insurance company have been unable to contact the other driver? Or that the other insurance company are not responding to your insurance company?
If you only have third party insurance, then your insurance company on not liable for any damage to your car. The party liable for those costs is the other insurance company (assuming he was insured, and that they honour any insurance he holds even though he was driving alone illegally).
If it turns out that he was not insured, then you may be able to make a claim against the Motor Insurers' Bureau - see
https://www.mib.org.uk/making-a-claim.