yum update return ssl error on centos 5.8

I want to install a package by doing yum install on my centos 5.8 64, but it returns SSLError: unknow protocol.
I know centos 5.8 is ancient but at the state upgrading is not my option, yet.

This is the error:

Traceback (most recent call last):
  File "/usr/bin/yum", line 29, in ?
    yummain.user_main(sys.argv[1:], exit_code=True)
  File "/usr/share/yum-cli/yummain.py", line 309, in user_main
    errcode = main(args)
  File "/usr/share/yum-cli/yummain.py", line 178, in main
    result, resultmsgs = base.doCommands()
  File "/usr/share/yum-cli/cli.py", line 345, in doCommands
    self._getTs(needTsRemove)
  File "/usr/lib/python2.4/site-packages/yum/depsolve.py", line 101, in _getTs
    self._getTsInfo(remove_only)
  File "/usr/lib/python2.4/site-packages/yum/depsolve.py", line 112, in _getTsInfo
    pkgSack = self.pkgSack
  File "/usr/lib/python2.4/site-packages/yum/__init__.py", line 662, in <lambda>
    pkgSack = property(fget=lambda self: self._getSacks(),
  File "/usr/lib/python2.4/site-packages/yum/__init__.py", line 502, in _getSacks
    self.repos.populateSack(which=repos)
  File "/usr/lib/python2.4/site-packages/yum/repos.py", line 260, in populateSack
    sack.populate(repo, mdtype, callback, cacheonly)
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 168, in populate
    if self._check_db_version(repo, mydbtype):
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 226, in _check_db_version
    return repo._check_db_version(mdtype)
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1226, in _check_db_version
    repoXML = self.repoXML
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1399, in <lambda>
    repoXML = property(fget=lambda self: self._getRepoXML(),
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1391, in _getRepoXML
    self._loadRepoXML(text=self)
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1381, in _loadRepoXML
    return self._groupLoadRepoXML(text, ["primary"])
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1365, in _groupLoadRepoXML
    if self._commonLoadRepoXML(text):
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 1201, in _commonLoadRepoXML
    result = self._getFileRepoXML(local, text)
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 974, in _getFileRepoXML
    cache=self.http_caching == 'all')
  File "/usr/lib/python2.4/site-packages/yum/yumRepo.py", line 811, in _getFile
    http_headers=headers,
  File "/usr/lib/python2.4/site-packages/urlgrabber/mirror.py", line 412, in urlgrab
    return self._mirror_try(func, url, kw)
  File "/usr/lib/python2.4/site-packages/urlgrabber/mirror.py", line 398, in _mirror_try
    return func_ref( *(fullurl,), **kwargs )
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 936, in urlgrab
    return self._retry(opts, retryfunc, url, filename)
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 854, in _retry
    r = apply(func, (opts,) + args, {})
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 922, in retryfunc
    fo = URLGrabberFileObject(url, filename, opts)
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 1010, in __init__
    self._do_open()
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 1093, in _do_open
    fo, hdr = self._make_request(req, opener)
  File "/usr/lib/python2.4/site-packages/urlgrabber/grabber.py", line 1202, in _make_request
    fo = opener.open(req)
  File "/usr/lib64/python2.4/urllib2.py", line 364, in open
    response = meth(req, response)
  File "/usr/lib64/python2.4/urllib2.py", line 471, in http_response
    response = self.parent.error(
  File "/usr/lib64/python2.4/urllib2.py", line 396, in error
    result = self._call_chain(*args)
  File "/usr/lib64/python2.4/urllib2.py", line 337, in _call_chain
    result = func(*args)
  File "/usr/lib64/python2.4/urllib2.py", line 565, in http_error_302
    return self.parent.open(new)
  File "/usr/lib64/python2.4/urllib2.py", line 358, in open
    response = self._open(req, data)
  File "/usr/lib64/python2.4/urllib2.py", line 376, in _open
    '_open', req)
  File "/usr/lib64/python2.4/urllib2.py", line 337, in _call_chain
    result = func(*args)
  File "/usr/lib64/python2.4/site-packages/M2Crypto/m2urllib2.py", line 82, in https_open
    h.request(req.get_method(), req.get_selector(), req.data, headers)
  File "/usr/lib64/python2.4/httplib.py", line 810, in request
    self._send_request(method, url, body, headers)
  File "/usr/lib64/python2.4/httplib.py", line 833, in _send_request
    self.endheaders()
  File "/usr/lib64/python2.4/httplib.py", line 804, in endheaders
    self._send_output()
  File "/usr/lib64/python2.4/httplib.py", line 685, in _send_output
    self.send(msg)
  File "/usr/lib64/python2.4/httplib.py", line 652, in send
    self.connect()
  File "/usr/lib64/python2.4/site-packages/M2Crypto/httpslib.py", line 47, in connect
    self.sock.connect((self.host, self.port))
  File "/usr/lib64/python2.4/site-packages/M2Crypto/SSL/Connection.py", line 174, in connect
    ret = self.connect_ssl()
  File "/usr/lib64/python2.4/site-packages/M2Crypto/SSL/Connection.py", line 167, in connect_ssl
    return m2.ssl_connect(self.ssl, self._timeout)
M2Crypto.SSL.SSLError: unknown protocol

Doing yum update resulting the same error as above.

I have done upgrading openssl to OpenSSL 1.0.2a 19 Mar 2015 but the error still the same.

What would be the fix, so I am able to use yum to install package?

Thank You.