You can monitor servers via ICMP (ping only) by modeling them as model type "Pingable". You can set your polling interval (default is 300 seconds but you can make it 60 seconds or whatever you like) as well as DCM retry intervals (default is 3000 ms with 3 retries). What you will want to make sure you do is set the "Value_When_Red" attribute to a non zero value (7 is the default for SNMP models and what I would recommend here). The default is 0 on a Pingable which will cause the icon to turn blue (initial) and not alarm. The idea behind that default is that folks would discover their network and include printers, desktops, etc. that they don't want to alarm on. If monitoring was "important", you'd have SNMP on it. Anyway, when you change the value to 7, you'll get red when it's down and green when it's up.
As far as notifying when it the server doesn't respond to ping in a 5 minute window, you could have Spectrum poll the device every 60 seconds and then configure a SANM policy to only notify after the alarm is 5 minutes old.