Software wise, you need Rslogix500 and Rslinx Lite.
In order to get the two communicating together, you will have a whole selection of variables to choose from...
some examples are;
Ethernet
Serial
DH-485
The most cost effective way to get an out of the box 1500 and a 5/03 processor talking is using DH-485. (allows up to 32 nodes)
Go to the AB website and query the communications options.
It has been a long time with the ML1500, but I think that you can use the Mini-Din cable pinout for the DH-485 connection as well.
In the SLC5/03, you will change your default settings on COM1 to DH-485. (And specify a node number, 0-31)
Your PC will be 0 usually in RSlinx when you setup your DH-485 driver.
Set your ML1500 to another node, ie (2) and browse in the linx window.
Communicating in the processor requires that you do messaging.
Read up in the manuals about messaging. There are several examples of what you are attempting to do on the AB website.
Come back again if you need more assistance,