@Monique862
The host is not allowed to change the price once you have already booked (providing you put in the correct number of people, dates, pets etc.) but they are completely entitled to change the price if you only sent an enquiry or a request to book. There is no contact yet at that point.
Are you sure you entered the correct number of people etc.? I am not sure where you are trying to book and if it's somewhere where Airbnbs are very cheap, but $1,227.93 seems insanely low for 12 people for 21 nights. Think about it, that's less than $5 per person per night.
If you entered a much lower number of guests, that would explain why the host came back to with a significantly higher price once realising how many people were coming. The $5,000 works out still to less than $20 per person per night, which sounds more realistic to me.
When you search for listings, it will give you a price based on the dates and number of guests. Even if the listing states a maximum capacity of 12 people or more, it won't necessarily show you the price for 12 if you put in a lower number than that as many listings have a base fee for, say, four guests, and than additional fee for each extra person. There may also be additional fees for cleaning, linens, pets etc. but you should also see those in the price breakdown ahead of booking.