You are right, there are many factors which go into the decision by a bank to give you a mortgage. However, at this time most banks allow you to use 25-32% of your gross income for the maximum monthly mortgage payment.
Since $5,000/mo. represents 20% of a $25,000 monthly gross income, both of your figures appear to be possible. There should be no problem to get a loan with a 20-25% down-payment at a 5-1/2% fixed interest rate (possibly lower) and a 30 year loan term, as you are now in jumbo loan territory.
The monthly mortgage payment of $5,000 at a 5-1/2% fully amortized loan would allow for a $900,000 loan and an approx. $8,000 monthly payment would be required for a loan of $1,400,000. Assuming a 20% down-payment of $225,000 would allow you purchase a home of $1,125,000 for the $5,000 monthly amount. Assuming a 25% down-payment of about $470,000 would allow a purchase price of $1,870,000 for the higher mortgage amount of $8,000.
As you can see, it is not just how much of a loan you can afford to get with your income, but also how much of a down-payment you can afford to put down.