CS5のアップデート不可による不具合ってありますか？

InDesignであれば、CS5の各バージョンのリリースノートはまだ残っています。

ただし英語です。

https://helpx.adobe.com/jp/indesign/indesign-releasenotes.html

いずれにしても、動作保証外かつ初期バージョンの場合、オウンリスクを前提に使う、ということになるとは思います。

ご認知済みであれば申し訳ないです。
Win 10はCS5を使用する上で動作保証外のOSとはなります。

2017年の記事でCS6に関しては動作することは確認されているようですが、
それから数年、Win10も様々なUpdateが出ているのでSilk-mさんの記載いただいた情報以外にも「予見できないトラブル」も大いにあると思われます。
https://helpx.adobe.com/jp/creative-cloud/kb/Windows_10_compatibility_FAQ.html

Illstrator の場合は 15.0.1、15.0.2 がありますが大きな問題ではなさそうです。

https://www.dtp-transit.jp/versions.html

Photoshop 12.0.4 のアップデート内容

For convenience and reliability, we highly recommend that you apply this update directly from within Photoshop. To do so, choose Help > Updates in Photoshop CS5 and apply all of the updates listed under Adobe Photoshop CS5 in the Adobe Application Manager.

This update applies to all languages EXCEPT Middle Eastern, North African French and Greek.

The 12.0.4 update enables specially designed apps on tablets, smartphones, and PCs to communicate with and control interaction with Photoshop CS5 (Located in the Edit menu: Remote Connections). Now you can be creative on other devices and instantly incorporate what you create into Photoshop. You must install the 12.0.4 update to activate a remote connection between Photoshop CS5 and any apps that Adobe or third-party developers create to interact with Photoshop. For example, Photoshop CS5 must be updated to 12.0.4 to interact with three new iPad apps that Adobe has designed to work with it - Adobe Nav, Adobe Color Lava, and Adobe Eazel. These apps will be available in the future on the App Store.

The 12.0.4 update also fixes liquify performance, type related crashes, and other top customer issues. The most significant fixes include the following:
- A number of potential security vulnerabilities have been addressed.
- Liquify save mesh now works as expected.
- An issue with Sharpen crashing has been fixed.
- An issue with Quick Selection crashing has been fixed.
- The Orphea Studio File Info issue has been resolved.

InDesign は使っていないのでわかりません。