Two little words, Surround View. This is a feature of all AMD chipsets since at least the 690G that allows the use of the onboard AMD graphics with an AMD video card to allow for the use of up to four monitors (or five now with the HD 5xxx series), with two connected to the video card and two connected to the onboard.
Unfortunately it looks like MSI hasn't enabled that feature in the bios for your motherboard despite the fact the chipset does in fact support it. Looking at the specs and the manual for your board I can't find any mention of it anywhere. It is possible that they have it enabled by default and just don't have the option in the bios. To give an idea here is a ssimilar spec'ed Asus board (same 880G/SB710 chipset) that does have it, ASUSTeK Computer Inc. - Motherboards- ASUS M4A88T-M
One way o see if it is enabled by default with the option not present is to go into the bios and set the "VGA Share Memory" setting to 128 MB, save and restart. If Windows detects the onboard upon restart, then it is just a matter of connecting the new TV to either the HDMI or VGA port, and you should be good to go.
If it isn't enabled by default or Windows doesn't see the onboard in addition to the 5570, then the only other option wit the layout of that motherboard would be a PCI card or something like this, Newegg.com - Jaton USB 2.0 to DVI-I External Video Adapter VIDEO-101USB -D
A PCI card can get messy with driver
conflicts depending on which card is used (too old or no Windows 7 support, and the driver for it cancels out the driver for the newer card). No idea how well those USB adapters work other than from reading user reviews, and they seem to be hit and miss.