Npm client looks like updated but does not update - node.js

Question

[grexlin85:~] >sudo npm i -g npm#latest
/usr/local/bin/npm -> /usr/local/lib/node_modules/npm/bin/npm-cli.js
/usr/local/bin/npx -> /usr/local/lib/node_modules/npm/bin/npx-cli.js
+ npm#6.13.7
updated 1 package in 5.748s
[grexlin85:~] >npm -v
5.8.0
[grexlin85:~] >sudo npm -v
6.13.7
Hello, I've updated my npm but if I write sudo npm -v it looks like updated but does not update and the version is still same. What can I do?
--------Edit-------
[grexlin85:~] >npm i -g npm#latest
npm WARN npm npm does not support Node.js v10.15.2
npm WARN npm You should probably upgrade to a newer version of node as we
npm WARN npm can't make any promises that npm will work with this version.
npm WARN npm Supported releases of Node.js are the latest release of 4, 6, 7, 8, 9.
npm WARN npm You can find the latest version at https://nodejs.org/
npm WARN checkPermissions Missing write access to /usr/local/lib/node_modules/npm
npm WARN checkPermissions Missing write access to /usr/local/lib/node_modules
npm ERR! path /usr/local/lib/node_modules/npm
npm ERR! code EACCES
npm ERR! errno -13
npm ERR! syscall access
npm ERR! Error: EACCES: permission denied, access '/usr/local/lib/node_modules/npm'
npm ERR! { [Error: EACCES: permission denied, access '/usr/local/lib/node_modules/npm']
npm ERR! stack:
npm ERR! 'Error: EACCES: permission denied, access \'/usr/local/lib/node_modules/npm\'',
npm ERR! errno: -13,
npm ERR! code: 'EACCES',
npm ERR! syscall: 'access',
npm ERR! path: '/usr/local/lib/node_modules/npm' }
npm ERR!
npm ERR! The operation was rejected by your operating system.
npm ERR! It is likely you do not have the permissions to access this file as the current user
npm ERR!
npm ERR! If you believe this might be a permissions issue, please double-check the
npm ERR! permissions of the file and its containing directories, or try running
npm ERR! the command again as root/Administrator (though this is not recommended).
npm ERR! A complete log of this run can be found in:
npm ERR! /home/grexlin85/.npm/_logs/2020-02-03T07_50_54_366Z-debug.log
I've tried without sudo and i get this output