Reading 68HC05 Eeprom
First do you know if it has been secured ?? If so then its hopeless.

Its been 20 years since I last used HC05. Where from my paper copy of the data sheet. It looks like you can likely use its Standalone Bootstrap mode by appling VPP followed by setting PD5 and PD2 low, along with PD3 and PD4 to high. Then release RESET# and the HC05's bootstrap with start dumping the PROM contents at 4800 baud 8N1 out the SCI(UART) assuming a 2 MgHz crystal, starting with $0020 through $1FFF. You could just convert this to RS232 and send to a PC's Serial Port. No need for an Arduino.

This is all assuming the PROM has not been secured.

Here is an article of someone doing just this for a 7085U. My above datasheet is for the 705C8.

Note, Near the end of the 705's popularity a variety of different models came out, like the "J" and "K" which had cheaper programers. So there may likely be differences. Find the datasheets. There likely is a Standalone Bootstrap for your version that can be triggered to dump out either the SCI(UART) or SPI.