Change the program and arguments to

<key>Program</key>
<string>/bin/sh</string>
<key>ProgramArguments</key>
<array>
    <string>sh</string>
    <string>-c</string>
    <string>while sleep 5; do /usr/bin/osascript -e 'tell application "System Events" to keystroke "g"'; done</string>
</array>

and change the sceduling to just run the process and keep it alive. I think the appropriate method is

<key>KeepAlive</key>
<true/>

Change the plist to

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"
 "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
    <key>Label</key>
    <string>G-key-pusher</string>
    <key>Program</key>
    <string>/usr/bin/osascript</string>
    <key>Program</key>
    <string>/bin/sh</string>
    <key>ProgramArguments</key>
    <array>
        <string>sh</string>
        <string>-c</string>
        <string>while sleep 5; do /usr/bin/osascript -e 'tell application "System Events" to keystroke "g"'; done</string>
    </array>
    <key>ServiceDescription</key>
    <string>Auto Keypress</string>
    <key>KeepAlive</key>
    <true/>
</dict>
</plist>

What it does, is to run a shell script that does the 5 second timer and calls osascript. The launchd plist just ensures the script is restarted if it were to die for some reason. Please note that I still haven't tested this, but I don't see any reason why it shouldn't work. Though I have had problems in the past when changing launchd items, which I fixed by changing the label. Which reminds me, you had omitted the value for the Label key in your plist.

(Edit: Explain a little, and provide a complete file instead of explaining what parts need to be changed.)