First of all, unless you paid sticker on a fully loaded G37, or have really crappy credit, I highly doubt your monthly payment would be $800 a month. Second, I don't think you fully understand how interest works, so let's work this out.

Let's say the final price of the car is $42,000:

financed for 60 months with $0 down at 0% interest your payment would be $700

Let's say you put $5000 down, your monthly payment would be $617, so that's an $83 difference per month.

Now, let's say you were to put that $5000 in a high yield checking account (the highest national rate is 6.31% APY). The account would give you about $26 a month in interest, making your true "out of pocket" difference only $57, for a total monthly payment of $674.

Now, you can pay that extra $57 out of the $5000 if you'd like (which would obviously lower your monthly interest earned a bit). Assuming you left the money in the account for the 5 years, your total "out of pocket" expenses would be $3420. Significantly less than $5000.

Anyway, I think you see what I'm getting at. Your down payment may lower your monthly payment a bit, but you know what? You're essentially giving infiniti finance an interest-free loan of $5000 for 5 years and getting absolutely nothing in return for it.