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You can check the tow capacity of the Explorer HERE. Basically it will depend on how the Explorer is equipped. If it has the Heavy Duty Towing Package, it is rated for 5000 lbs when a weight-distributing hitch is used. If not, it can only tow 2000 lbs and that is insufficient for either of the trailers you are considering.
As I said, it depends on whether your Explorer has the factory Heavy Duty Towing Package or not. If it does, AND you use a WD hitch, you are fine. If not, the WD hitch does not make it ok.
MarkB - depending on how old the explorer is, you might be able to use the following to see your sticker equipment.
http://fordlabels.webview.biz/webviewhybrid/WindowSticker.aspx?vin=entervin