Technically no, not all 3 at the same time. you would need to use a DP to HDMI active adapter, then it would work fine.
Three monitors or more on any 5000, 6000, 7000 or R7-R9 series card require that one is through the Displayport (or miniDP) and that you are using Windows Vista or Windows 7 and 8, 10. If your monitors do not have a native Displayport then only an active Displayport to DVI adapter will work. A passive adapter will give display when using two monitors but when using three it must be an active adapter. Active adapters have additional circuitry inside of them to translate the Displayport signal to something that DVI or HDMI can understand. A passive adapter is just piggybacking off of an existing output from another port which is why it does not give you an additional display. If you just got your monitors then it is probably best to get monitors that have Displayport on them. They are not any more expensive. You just need one that has Displayport. If you already had your monitors and prefer to use them then you will need an active adapter. Active Displayport to DVI is available at http://www.newegg.com
-998-051 and active mini Displayport to DVI is available at http://www.newegg.com/Product/Product.aspx?Item=14-998-050. These adapters will support any resolution up to 1920x1200. If you are using a display that uses only HDMI then you would use one of these adapters with a DVI to HDMI adapter or DVI to HDMI cable plugged in to it. There are no active Displayport to HDMI adapters. You can find the supported monitor configurations at http://support.amd.com/us/kbarticles/Pages/gpu50-ati-eyefinity-display-connectivity.aspx. Thank you. Mark