I have been wanting to visit Mexico:
The problem is there is a lot of cities, it would be my first time going there and I'm having a hard time deciding between which ones:
- Oaxaca city - my understanding is there is good food here
- Guadalajara
- Mexico City
- Mazatlán
- Sinaloa

For Budget:
$100 for hotel per night
up $500 for flight
$75 for transportation per day
$150 for food per night

Duration: 5 days
I would be flying solo, I have an idea of what I can do in each city. Just wanted to get some nuanced perspectives from the community
Thanks

What time of year? Start with Mexico City, research your flight costs. I don't think the other costs will be difficult to attain. There are many trip reports here on Fodor's worth browsing.

Random thoughts.
Like mlgb asks, what time of year? Mazatlan will be hot & humid during the summer.
How's your Spanish?
What are your primary interests? Food? Archeological sites? Museums? Colonial architecture?
Sinaloa is a state, not a city, and is experiencing quite a bit of violence & cartel activity lately.
You could easily fill 5 days in either Mexico City or Oaxaca.
Mexico City is fascinating, but maybe a bit overwhelming for a 1st timer to Mexico. Unless you do some guided tours.
Guadalajara is my least favorite city in Mexico. 2 days was enough for me. Although you could probably supplement a visit there to one or 2 of the nearby Pueblo Magicos.
Apart from the airfare, with your budget, you can probably do all that for about half of that amount if not less. Unless you want 5 star everything.
Another option for 5 days would be Guanajuato & San Miguel de Allende. Flying into/out of bjx/Qro.
And yet another option would be Puerto Vallarta. Some people have traveled there for 3 decades and never bother to go anywhere else in Mexico. Fugly weather in the summer, however.

up $500 for flight
Where are you flying from?

That seems an awfully big daily budget for transportation and food.

I agree with baldOne that Mexico City might be daunting, however, if you pick a quieter neighborhood, La Condessa or Roma Norte it could be fine. Also CDMX has Uber which we use a lot when we are there. Oaxaca, last year, didn't have Uber, they did have something called DiDi, I think but it wasn't as good as Uber. Guanajuato is one of my favorite placed in Mexico, but it would be a different experience. If you have already done some traveling, and have been in other big cities you can handle Mexico City. Good luck

How's your Spanish? Don't speak it.
What are your primary interests? Food / Museums / Sports
Guess Mexico City and Oaxaca would make sense for 5 days.