Lodging for family of 5

You are going to have to look for a family room for five. That can be limiting. Personally I think you would want two rooms -- 2 and 3 -- BECAUSE that gives you two bathrooms. Five people and one bathroom is a little tight. Steves has a number of good recommendations in his Paris guide book. Start there.

Hard to find rooms for 4; for 5 you are looking at a suite.

I might choose an area like Montparnasse/14th east of the station and see if some of the small hotels would have a triple and a double in your price range. Or just run a request on hotels.com for 5 people 2 rooms and see what you come up with in your price range and get feedback here. For a first visit, I'd be looking at the Latin Quarter or Marais if you can find something you can afford or as I noted Montparnasse is filled with amenities and fairly convenient -- we would walk through the Luxembourg Gardens on our way to the center and it was lovely.

Firstly, you are extremely unlikely to get a reservation 2 1/2 years in the future. And prices for this year may not (likely will not) be the going rate in '25. At best you may find a few possibilities that you can track, and then book a year or so in advance.

Have a look at hotels or apartments on something like booking.com. Use the filters for price, location, # of beds, etc. You may find that you will need 2 hotel rooms. Given your budget, you may find that an apartment will be a better value.

Thank you! Not reserving yet, but want a good game plan, thanks for the info!

Too early to even consider. I expect hotel prices to rise significantly next year due to the 2024 Olympics. Once that occurs, prices for 2025 will not likely drop much. Early 2023 will likely be a completely different hotel landscape than what we can expect for 2025.