How much would you pay for a 2016 Mazda-Cx 5 GT sport with 104k miles?

Hi, I’m looking to buy my first car ever. I test drove a 2016 Mazda CX-5 last summer and loved it! Right now my budget is $12k at the highest including all fees and taxes. I’m paying in cash. I saw a 2016 Mazda cx-5 GT sport listed for $13.1k with 104k miles. The car’s been on the lot for 114 days. According to the car fax report it has 1 owner and no accidents. Regular maintenance and the dealership recently did maintenance on the vehicle. I feel like $13k is too high for a 10 yr old car with over 100k miles.

I was thinking to email dealership and say:

*Hi, I’m very interested in the 2016 Mazda CX-5 Grand Touring. I noticed it’s been on the lot for a while, and I’m prepared to make this very easy. I’m paying cash and my total budget including tax and all fees is $11,500 out the door. If we can make that work, I can come in immediately and complete the purchase. Please let me know. My phone number is: Xxx-xxx-xxxx*

Is that too delusional or is it better to see the car in person and then negotiate? I found a car with the same trim except it in includes the technology package from a private seller. Single owner, for $10.5k with 116k miles. I just feel like I might not be taken seriously as a woman and first-time buyer.