The faster timing signals somehow did it. Better accelerators look like a stock 68000 to the motherboard and peripherals for compatibility reasons. IIRC, AdSpeed was not completely buffered. Also, the A570, which is a add-on CDrom drive sidecar (gives the A500 CDTV-like functionality), might be somewhat delicate.
SysInfo.lha is the archive. After ypu de-archive it, SysInfo is the executable. SysInfo.info is the icon for the program. There will probably also be document and hystory files, too. They should all be in the same directrory together. You could even copy them to the ramdisk or to a floppy for permanent keeping. Simply double click the icon.
If there is no icon, you will have to use cli or a shell. At the prompt, CD to the directory where you de-archived SysInfo. At the next prompt, type Sysinfo.
The program should execute.
SysInfo simply measures performance and reports that and info about installed hardware and libraries.