LGPLv3 section 5

I'm not sure, but there may be a confusion happening. You are taking an LGPL library (let us call it "L") and combining it with other libraries, themselves under BSD and MIT licences (let us call these libraries "B" and "M" respectively), to produce a new library (let us call it "Z"). In addition to combining L with B and M, you may be making modifications to L during this process.

When s5 refers to "the Library" (note the capital, which is significant) it is referring to L. When it says that you must "accompany the combined library [that is, Z] with a copy of the same work based on the Library, uncombined with any other library facilities, conveyed under the terms of this License." it means you when you give someone a binary copy of Z, you must also provide the source of L, with any modifications you have made to it during this exercise, unencumbered by the source of B and M, and you must convey this source under LGPL.

You do not have to provide the source of B and M, even though they are freely-licensed (though of course you may if you choose). You will also have BSD, MIT, and LGPL s5b obligations with respect to the distribution of Z, which I do not discuss here.

As Bart notes, if you have actually edited B and M into the source of L, rather than just combining (possibly modified versions of) B, M, and L into a single library Z, this analysis doesn't apply.

Does section 5 of LGPLv3 apply to opensource library like mit, bsd based based library as well?

The LGPL license does not contain an explicit exemption for other open-source (or even other LGPL) libraries, so section 5 equally applies to open-source libraries.

However, this does not mean it has to be very onerous to comply with section 5.

If you organize your repository such that each independent sub-library is located in a folder-tree of its own, then you have the uncombined code readily available for inclusion in a distribution and for referring people to. When you tell people where to obtain source code, there is nothing preventing you from stating that the code is in sub-folder X or repository X.

Note that if you have created something that is so interwoven with the original LGPL library that you cannot put sub-libraries in separate folders, then chances are that your work doesn't fall under clause 5 anyway.

All licenses which are compatible with the GPLv3 are also compatible with the LGPLv3 and AGPLv3.

All licenses which are compatible with the GPLv2 are also compatible with the LGPLv2.1.

"Compatible" here means that you can fulfill the conditions of both licenses, without it conflicting with the conditions of either.

In this case, the MIT license, BSD-2-clause and BSD-3-clause licenses are all compatible with GPLv3, LGPLv3, AGPLv3, GPLv2 and LGPLv2.1.

So, code licensed under the former can be copied into the latter or linked with the latter (statically or dynamically), and distributed together, as long as the conditions of all the included licenses are fulfilled.

The Combined Libraries clause of Section 5 of the LGPLv3 and Section 7 of the LGPLv2.1 is completely unnecessary and redundant for software licensed under compatible licenses. Rather, it is meant for software licensed under incompatible licenses like proprietary licenses and incompatible open source licenses.

For e.g. the Apache License v2.0 is compatible with GPLv3, LGPLv3 and AGPLv3 but it is incompatible with GPLv2 and LGPLv2.1. The reason for Apache License v2.0's incompatibility with GPLv2 (and LGPLv2.1) is explained in this answer.

A library licensed under Apache License v2.0, like OpenSSL 3.x, is never usable by a software licensed under GPLv2-only due to this incompatibility.

However, a library licensed under Apache License v2.0, like OpenSSL 3.x, is usable by a software licensed under LGPLv2.1-only, as long as the conditions of the Combined Libraries clause of Section 7 of the LGPLv2.1 is fulfilled. This is explained in this answer.

OpenSC's libp11 is an example of this. It is licensed under LGPLv2.1, and it uses OpenSSL which is licensed under Apache License v2.0. Both libp11 and OpenSSL are open source software with publicly available source code on the Internet, and they are cleanly separated with dynamic linking. So, the conditions of Section 7 of the LGPLv2.1 are very easily fulfilled.