New to real estate investing.  I'm sixty years old and was toying with the idea of investing some of my retirement money in a home on Cape Cod.    Can I even break even if Summer rental season is a max of five months,...

If you only have 1 MTR and don't mind listing on different platforms and managing the calendar yourself it's doable but the functions aren't feasible for large portfolios of MTRs. 

I rent out my spare bedrooms and it allows to increase my rental income by about 25%I did but I don't think it's feasible for me.

A year or 2 it was more feasible to get something decent for under $100K in some of the more affordable markets, but even those markets are now over $100K.

I'm looking to do an owner occ for my first deal because this is the most feasible way for me to take my first step in REI. 

They should be able to give you what is feasible with what you have. 

I don't have direct contact in the Acquisitions department as I work with their environmental due diligence team on Phase I Environmental Site Assessments.That said, I echo @Chris Martin in warning that the environmental and engineering feasibility process can easily take a year or more.  

It is totally feasible for you to self manage, even if you're just getting started.

I'm in a similar situation but need more inputs to figure out if it is feasible for me.

Now, if you do become lenient due to credit score or past rental history because they gave you a feasible explanation, then make sure they have some stake in it.