Not really, as long as you are up front with a lender, most would just require you to show them the establishment of the LLC/accounts and then could proceed with that.

we had that property under 2 years and we pay a lot of mortgage. 

Lenders will evaluate whether you are able to pay. 

Lenders will not take a risk of 90-95% on your deal. 

Did you work with any real estate professionals (agents, lenders, etc.) that you'd recommend to others?

If you were either the buyer, seller, lender, or realtor in a Loan Assumption transaction in New Jersey, I'd love to connect and ask you a few questions.  

This guideline is lender specific.

Mortgage payment is ~$5000 per month

My thought process is to purchase the property initially under my name so that we can pay 5% down as my understanding is that mortgages to LLCs are more difficult to find, have higher interest rates, and require a higher down payment (around 25%).

You should be able to break even on mortgage payments.