Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
If the automobile driver is at fault, you can go after him/her personally for what is not covered by insurance. You should consult your own lawyer to protect your legal rights.
Assuming the other party was at fault, his insurance carrier is contractually obligated only to pay the maximum $5,000 under the policy. He (the other party) would be obligated to make up the difference. However, make sure that you do not sign a property damage release for the $5,000 from the insurance carrier before you get that $3,000 since that may bar you from trying to collect the other $3,000. Better yet, try to accomplish both at the same time. He pays you $3,000 at the same time that the carrier pays $5,000. If the other party has no money, then you may be out of luck with regard to the other $3,000. If you wish to keep your bike, and you manage to collect money from both, there will be a deduction for whatever the salvage value is. If you were injured, you may be able to collect enough money from the injury claim to make up the difference. Since you did not mention an injury, I am assuming that was not the case.
The other driver is liable for the $8k total damages, even if he only has $5k in coverage. He is then responsible to pay the remaining $3k. However, given that he did not have any more than $5k in property damage coverage, he probably doesn't have much in the way of assets to pay the additional $3k. You will need to probably make payment arrangements with him to pay the difference.
You can sue him in Small Claims court for the difference in what was not covered. Also, San Diego county provides free Small Claims legal advisors to help with each step from 8:30 am to 4 pm Monday - Friday.
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