One option would be to use 5K and put on the car loan. (How many months of expenses would 10K left in the EF provide?)
Then maybe lower the amount extra you are putting on your mortgage and investing in the market to be able to come up with an extra 416 dollars a month to put towards the car loan. Then it would be paid off in a year.
What is your mortgage rate at?
Mathematically it makes sense to throw more money at a higher interest rate loan or invest in something that will provide a greater level of return than debt repayment. But, it would be nice to have one less bill a month too.
At the end of the year, you could split the difference between what the car payment was and refund your emergency account/pay extra on the mortgage, or invest.
Or just invest it all now, make minimum payments on everything, hope you never need the emergency fund, and hope the market doesn't tank. But I prefer the combination approach of investing, saving, and paying off debt early. Because the best mathematical approach doesn't care about what is best for you, and what the future might bring. Good to have all your bases covered.