LDAPS SSL Handshake failure..

The fact that the server (F5) is sending an immediate Alert right after the ClientHello message indicates that the server is not in some way compatible with the client's choice of protocol, ciphers, and potentially TLS extensions. Let's look is the most obvious thing first: the ciphers. The "unknown" ciphers in your list are simply unknown because ssldump doesn't know what to call them. You can actually look them up by their hexadecimal number here:

http://www.iana.org/assignments/tls-parameters/tls-parameters.xhtml

So let's rewrite that list with the real names:

TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384
TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA
TLS_DHE_DSS_WITH_AES_256_GCM_SHA384
TLS_DHE_RSA_WITH_AES_256_GCM_SHA384
TLS_DHE_RSA_WITH_AES_256_CBC_SHA256
TLS_DHE_DSS_WITH_AES_256_CBC_SHA256
TLS_DHE_RSA_WITH_AES_256_CBC_SHA
TLS_DHE_DSS_WITH_AES_256_CBC_SHA
TLS_DHE_RSA_WITH_CAMELLIA_256_CBC_SHA
TLS_DHE_DSS_WITH_CAMELLIA_256_CBC_SHA
TLS_RSA_WITH_AES_256_GCM_SHA384
TLS_RSA_WITH_AES_256_CBC_SHA256
TLS_RSA_WITH_AES_256_CBC_SHA
TLS_RSA_WITH_CAMELLIA_256_CBC_SHA
TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA
TLS_DHE_DSS_WITH_AES_128_GCM_SHA256
TLS_DHE_RSA_WITH_AES_128_GCM_SHA256
TLS_DHE_RSA_WITH_AES_128_CBC_SHA256
TLS_DHE_DSS_WITH_AES_128_CBC_SHA256
TLS_DHE_RSA_WITH_AES_128_CBC_SHA
TLS_DHE_DSS_WITH_AES_128_CBC_SHA
TLS_DHE_RSA_WITH_SEED_CBC_SHA
TLS_DHE_DSS_WITH_SEED_CBC_SHA
TLS_DHE_RSA_WITH_CAMELLIA_128_CBC_SHA
TLS_DHE_DSS_WITH_CAMELLIA_128_CBC_SHA
TLS_RSA_WITH_AES_128_GCM_SHA256
TLS_RSA_WITH_AES_128_CBC_SHA256
TLS_RSA_WITH_AES_128_CBC_SHA
TLS_RSA_WITH_SEED_CBC_SHA
TLS_DHE_RSA_WITH_AES_128_CBC_SHA256
TLS_ECDHE_RSA_WITH_RC4_128_SHA
TLS_ECDHE_ECDSA_WITH_RC4_128_SHA
TLS_RSA_WITH_RC4_128_SHA
TLS_RSA_WITH_RC4_128_MD5
TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA
TLS_ECDHE_ECDSA_WITH_3DES_EDE_CBC_SHA
TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA
TLS_DHE_DSS_WITH_3DES_EDE_CBC_SHA
TLS_RSA_WITH_3DES_EDE_CBC_SHA
TLS_EMPTY_RENEGOTIATION_INFO_SCSV

Based on: https://support.f5.com/kb/en-us/solutions/public/13000/100/sol13171.html, we know that 11.5.3 has a DEFAULT cipher string of this:

!SSLv2:!EXPORT:RSA+AES:RSA+3DES:RSA+RC4:ECDHE+AES:ECDHE+3DES:ECDHE+RC4:-MD5:-SSLv3

which looks basically like this (using the 'tmm --clientciphers' command):

AES256-SHA256  
AES256-SHA
AES128-SHA256    
AES128-SHA      
DES-CBC3-SHA       
RC4-SHA       
ECDHE-RSA-AES256-SHA384 
ECDHE-RSA-AES256-CBC-SHA 
ECDHE-RSA-AES128-SHA256 
ECDHE-RSA-AES128-CBC-SHA
ECDHE-RSA-DES-CBC3-SHA 

There are at least 7 matches between the two lists, so perhaps the best first question to ask is, what cipher string are you using in your client SSL profile? You're requesting TLS1.2, so don't think that's an issue. What does your client SSL profile actually look like?