New iMac takes minutes to startup

Remove login items then restart to test.

System Preferences > Users & Groups > Login Items

If it's not a login items issue, please download and run Etresoft: EtreCheck

Then copy and paste the results in your Reply.

No personal data is shared and that will give us a better idea of what's taking your Mac so long to startup.

How to fix slow shutdown and startup times. | MacTip.net

Fix slow start-ups in OS X | MacFixIt - CNET Reviews

Ways to help make a slow Mac faster

17 Reasons Why Your Mac Runs Slower Than it Should

Slow Mac Performance? This Article Solves It!

Fix slow start-ups in OS X | MacFixIt - CNET Reviews

6 Easy Tips to Speed Up OS X Yosemite on Your Mac

Avoid using any third-party software that claims to clean up your computer. Usually this software does more bad than good. Furthermore, you don't need it. Note that all computers will become slower over time even under normal use. Experienced users typically erase the hard drive and do a clean install from scratch at least once a year or whenever installing a major OS upgrade. Of course doing so also means you must maintain regular and multiple backups.

Add more RAM or cut back on the number of concurrently running applications and utilities. Remove unnecessary software such as anti-malware and software that promises to clean your Mac. Check for runaway processes: Runaway applications can shorten battery runtime, affect performance, and increase heat and fan acti… Also see:

Mavericks and later

Open Activity Monitor in the Utilities folder. Select All Processes from the View menu. Click on the CPU tab in the toolbar. Click twice on the %CPU column header to display in descending order. If you find a process using a large amount of %CPU, then select the process and click on the Quit icon in the toolbar. Click on the Force Quit button to kill the process. See if that helps. Be sure to note the name of the runaway process so you can track down the cause of the problem.

One Possible Cause for a Slow Computer

(Thanks to EtreSoft for this contribution.)

If you have a problem with a slow machine and are using Google Docs, then check if the Google Docs page is showing in top sites in your browser. Once it gets into Top Sites, you get a Safari Web Content process that slows down your entire machine, but you don't even get a window for it. That's the key point. The problem will not be definitively solved until you remove the Google Docs page from Top Sites.

[This has been modified for clarity and syntax by Kappy.]

Please take each of the following steps that you haven't already tried. Test after each one. Back up all data before making any changes.

1. Set the default startup disk.

2. Disconnect all wired peripherals except those needed to start up. If there's no change, reconnect them

3. Reset the System Management Controller.

4. Reset the PRAM. Afterwards you'll need to repeat Step 1.

5. Reset the printing system.