Firewalls and Anti Virus programs are only insurance measures, there not brick walls. Most infected computers have both running, the ones that don't simply have more infections. Once AVG moves a file to the vault it's renamed and the operating system can't use it so it's harmless to you. You may want to empty the AVG virus vault. Since the computer is slow run a malwarebytes scan, & Ccleaner. Take control of the programs starting up unnecessarily with windows, do a defrag.

Exploit-PDF.a is a detection for a specially crafted PDF file that exploits the Adobe Acrobat Mailto Unspecified PDF File Security Vulnerability to execute malicious code on a computer.

Update your adobe reader program, or install an alternative PDF file reader like Foxit Reader.

Here is a link that might be useful: adobe reader

this is why I warn people about opening any pdf file. Many of the new infections are coming through pdf exploits. When wanting to view a pdf file it is best not to let it just open in your browser or email but instead to choose to download it to your pc then right click on it and scan it with your antivirus program and malwarebytes. That way the infection can be caught before the file is opened.

If you are not using the secunia tool to keep your system up dated then you should do that. Adobe and java and flash all have had recent updates that are critical security updates.

As zep said scan asap with malwarebytes free and allow it to clean anything it finds. Trojans are much more likely to be caught by malwarebytes than by an AV.
How to download and install Malwarebytes' Anti-Malware application for Windows computers
Secunia Online Software Inspector (OSI)

and doing occasional online virus scans to make sure nothing has altered your AV that is on your pc is a very good idea.
ESET Online Scanner

more on pdf exploits and why you need to be very aware of these and how to prevent them
New PDF Exploit May Be First Of Many In The New Year, Experts Say
PDF exploit requires no specific security hole to function

I personally have chosen to remove adobe reader from my windows computers and am now using pdf-xchange instead which has not had the same security issues as adobe and foxit.
PDF-XChange Viewer 2.054
of course keeping any pdf reader updated is essential as is keeping the windows updates installed.

Thanks to both responders.
Steve