Are there codecs or codec packs? I have a video without any problem in Windows (with K-Lite Codec Pack, but probably it is not important).

I copied it into my smartphone with OS Adroid 5.0.2, and I indeed need some codec/codecs for playing it back, because I got a message that is not possible to
playing it back.

I know that there are media players with embedded codecs but it is not a solution for me - I want playing it back with my favorite media player.

Converting it to another (supported) format is not acceptable, too.

Is there a codec for it? Here is MediaInfo output for it:

General
Complete name                : C:\Videos\Woods.avi
Format                       : AVI
Format/Info                  : Audio Video Interleave
File size                    : 43.2 MiB
Duration                     : 2 min 59 s
Overall bit rate             : 2 050 kb/s
Writing library              : VirtualDub build 24469/release

Video
ID                           : 0
Format                       : MPEG-4 Visual
Format settings              : BVOP1
Format settings, BVOP        : 1
Format settings, QPel        : No
Format settings, GMC         : No warppoints
Format settings, Matrix      : Default (H.263)
Muxing mode                  : Packed bitstream
Codec ID                     : DX50
Codec ID/Hint                : DivX 5
Duration                     : 3 min 15 s
Bit rate                     : 1 977 kb/s
Nominal bit rate             : 3 695 kb/s
Width                        : 640 pixels
Height                       : 480 pixels
Display aspect ratio         : 4:3
Frame rate                   : 25.000 FPS
Color space                  : YUV
Chroma subsampling           : 4:2:0
Bit depth                    : 8 bits
Scan type                    : Progressive
Compression mode             : Lossy
Bits/(Pixel*Frame)           : 0.257
Stream size                  : 41.6 MiB (96%)
Writing library              : DivX 5.2.1 Beta (UTC 2004-09-08)

Audio
ID                           : 1
Format                       : MPEG Audio
Format version               : Version 2
Format profile               : Layer 3
Format settings              : Joint stereo / Intensity Stereo + MS Stereo
Codec ID                     : 55
Codec ID/Hint                : MP3
Duration                     : 2 min 59 s
Bit rate mode                : Constant
Bit rate                     : 64.0 kb/s
Channel(s)                   : 2 channels
Sampling rate                : 22.05 kHz
Compression mode             : Lossy
Stream size                  : 1.32 MiB (3%)
Alignment                    : Split accross interleaves
Interleave, duration         : 40  ms (1.00 video frame)
Interleave, preload duration : 502  ms
If you use an Android device with Google Play Services, Google has a document which requires what the device MUST have:

Current Android Compatibility Definition Document - 5.3 Video Decoding 

As you have an Android 5.0 device this document would apply:

Android 5.0 CDD - 5.1.3 Video Codecs

Note that your video file is an AVI container format which isn't listed so it would be up to the manufacturer to support that format or any additional codecs.

As to why can't you just add a codec see this StackOverflow post:

Adding video codec to Android

The short version is that codecs are in ROM and you can't write to ROM unless you are creating your own Custom ROM.

TL;DR: No, you can't add codecs. Use a third party player which supports your format or convert your video to a supported format (both of which you've rejected).