If the car's on HP then you can't legally sell it as its not yours. I'm wondering if the €5000 extra was the interest and cost of the HP agreement. If you hand back the car it will be sold at auction for considerably less than you paid for it - even selling privately you are unlikely to get the same price as you paid. You then owe the balance on the HP agreement.
If you could get somebody to buy the car then i would approch the hP company and advise them of your situation and check whether they might be prepared to do a deal by allowing you to sell the car and pay the balance yourself (likely to be a few K). you should get a rebate on the interest as you'll be paying it off before the term is up (e.g paying off in 6 months rather than 5 years). If you haven't got the money then they might be prepared to do a deal with you to convert the balance to a loan and allow you to pay back over time. Either way you are still likely to be losing money so it might if possible be better keeping the car for the moment.
There is also a half-way rule where you can hand back the car after paying half and depending how far into the agreement you are it might be worth considering this.
The additional €5k doesnt include interest. This is how it works.
New car - €25,000
Less Trade in - €5,000
Plus Settlement - €10,000
= Finance amount - €30,000
You cannot finance more than the car is worth so max finance allowed her is €25,000, so customer short €5,000 and needs to put down €5k as a deposit up front.
So the salesman says the new car is worth €30,000 in order to allow the customer to finance €30,000.
But now the cus owes €30,000 for the car and its only worth €25,000. It means he will be in a worse position when he trades it in as the settlement will be way above what the garages will give him for it.
OP said he has only made a couple of payments on the car. Bank can reposses and sell the car if less than 1/3 paid, cus can hand it back of more than 1/2 paid.
If it was done over 5 years at 8% total amount repayable would be €36,600, as far as i can remember a settlement figure is calculated under the Rule of 78, which gives a 5% discount for early repayment. I reckon the OP will still owe about €33,000 (perhaps someone could do this more accurately)
The OP can get a settlement figure by calling the bank and can see where he stands, but either way will owe a good few thousand more than he will sell the car for.
He can sell it but in order for title to pass he must clear the total amount outstanding on the HP agreement.