I am going to have a detached garage built in the back corner of my lot which is about 100' away from where we believe the current sewer line leaves the house. The existing sewer line leaves through the basement floor which is approx 5' beneath grade and then the connection to the city sewer is another 60'. Would I be able to connect to the existing (cast iron lines) or should I look at replacing everything while we are at it?

You will be OK with connecting to the existing sewer line somewhere in front of your house.

You will need about 25" + of slope for your new 3" sewer pipe. With 60" of depth ( existing sewer ) you should be OK with slope as well. Therefore, there is no need to upgrade existing sewer pipe all the way to the street.

Good luck with your project... Milo