This app was mentioned in 3 comments, with an average of 1.00 upvote
OK, so if the repeater doesn't support echolink, it's back to the drawing board. For what it's worth, to talk to echolink from your house, use this: https://play.google.com/store/apps/details?id=org.echolink.android&hl=en instead of an expensive echolink transceiver.
So with no echolink, how about going back to the idea of using a crossbander. Read this for a primer: http://www.qsl.net/wb3gck/cbr.htm
You will not regret investing in a good mobile radio. Put it in your car in a quick release bracket. use it when you drive around, then bring it into the house and run it as a cross bander when you want to work handheld.
As a bonus, you can also use it when out shopping, hiking, or other activities away from home.
For your UV-5R, you can talk on FM repeaters that ALSO support Echolink. This won't allow you to talk on other Echolink repeaters, but just Echolink users who have connected to the repeater via the Echolink software via their computer/phone/radio. Over 6,000+ users are connected at any given time world wide to the Echolink servers. You don't have to do anything special with your Baofeng. Either the repeater you've chosen supports it or it doesn't. Your Baofeng does not explicitly have Echolink capabilities.
Otherwise, to get the full benefits of Echolink and to get started you can
1) Go to the echolink website, create an account, get verified and install the Echolink software. If your computer has a microphone and some speakers, you're all set.
AND/OR
2) Download the Echolink app on your Android or iPhone. Create account and get verified if you didn't do option #1 above yet. If you did, just download the app and login. You can PTT and listen all through your phone using the screen.
Both of these options are free. Some people think it's dumb, but I think it's definitely a fun little corner of amateur radio, especially for those who are just technicians without HF permissions, or any class amateur who just wants to talk worldwide using the internet as an intermediary. Even if it is just the same as calling someone using VoIP or a conference call, the value is that there are other amateurs on the other end.
echolink the android ham-radio voip app