No one has discussed the factor of how long the OP plans to keep the car. That does make a difference. Strongly consider that.
If we're looking for sound financial advice, that's beyond the scope of this forum so I'll stick to the basics (some of which have already been covered):
1. Sounds like the OP (original poster) is finding a way to have lower monthly payments and has figured out a way for the mileage to not be a restriction. If the goal is for lower payments, it's not necessary a matter of lease vs finance. The bigger picture is car cost. The Mazda CX-5 ranges dramatically from $21k - $31k ish. If you can't afford the more expensive one, there's absolutely nothing wrong with that. Live below your means and you'll feel a lot more comfortable.
2. The car is only a portion of the overall cost of the car. Please don't forget insurance costs, gas and registration. When budgeting for a car, I knew I was expecting to drive over 80 miles per day. I typically had spent at least $250-300 in gas per month. That's pretty substantial and definitely limited what I could spend on the actual car. In fact, I was spending more in gas alone than the monthly finance payment for the vehicle. If you drive a ton, that might be the case. It might sounds stupid, but it is what it is. It doesn't matter how it's broken down. Think of the total cost per month with gas, payment, insurance included.
3. You may be in a different place financially at the end of the end of the lease. $3,000 may mean more to you now vs later -or- later vs now. Depends on what else is going on in your life, other obligations, etc. If you're getting married, having kids, then maybe $3,000 means a lot more to you now vs 3 years down the road. Just an example that came to mind, but I'm sure you can think of others that are applicable to you.
People thought it was silly that I took a loan out for a $1,700 scooter when I had money in the bank. Even my wife was like, "What? I'll just give that to you." Why did I do it? I had just lost my job and I was more in need of immediate savings (vs driving a car) that I wanted to realize ASAP. Most would buy a $1,700 scooter outright and enjoy the gas/insurance savings (vs a car) in a year or two). It takes awhile to start realizing savings after spending $1,700 at once. For me, by financing it, I was saving money the same month I bought the scooter. I had planned to sell it in a few years and would get most of my money back and by then I'd certainly have more income and the $1,700 wouldn't be that big of a deal. In my example, $1,700 meant more to me at the time of purchase than later. For that reason I made payments, meaning I consciously decided to pay little by little even though it would amount to a total higher cost when all was said and done vs buying it in cash all at once.
Many people in 2008 thought they were saving money buying a scooter when in fact, it took them years (longer than the time it took for the market to correct and probably longer than it took to find a replacement source of income) to realize any savings. Most weren't looking at $1,700 used scooters. They were buying $3,500 ones. You're not saving a single penny until you save enough to cover the $3,500 first.