There are many heater hoses that are 5/8" on one end and 3/4" on the other.
This could be one, don't know the exact sizes.
Anyway, make a pattern of your hose out of some brake line or something stiff and go to your local REAL parts store (not a McParts store like the Zone) and ask to see their hose selection and they will be happy to let you go thru them to find something that will work.
Now, often you will buy a longer hose than you need and cut it to length. My brother sells moulded hoses like the originals for 50's and 60's Buicks made from hoses right off the rack at the local parts store. He spent the time to hunt them down, he now buys hoses for late model applications and cuts them to length to fit right on the old Buicks.
At the NAPA store I worked at we had hundreds of these hoses, heater and radiator and would do this all the time for people. You would be very surprised at how many vintage cars radiator hoses can be made up this way.