Not necessarily the router...
Routers don't tend to slow down, you may be experiencing more interference from other nearby networks, or other wireless devices that don't use WiFi but operate in the same frequencies. If this is the case, a new router won't necessarily improve things, it will operate in the same frequency ranges as the Airport. Also, if using Cable internet, more neighbors may be on the network which tends to slow things down, particularly in high use times.
The AP Extreme AC router is dual band (2.4 and 5GHz). 2.4 has longer range, but operates in the same frequencies that wireless landline phones, bluetooth devices, wireless keyboards and mice, radars, and microwaves to name a few. And, 2.4 is considerably slower than 5GHz. Because the range is farther, neighbor's routers may overlap with your router. All of these tend to slow things down.
5GHz has a shorter range and suffers less from interference with other devices, and offers speeds up to 10x that of 2.4Ghz. You are less likely to see neighbor's 5GHz networks due to the shorter range, but might not reach all areas of your home (without additional access points).
The problem is, most of us accept defaults when setting up our gear, using the same SSID for both frequency bands and therefore we have little control over which frequency our devices will use, often falling back to the 2.4GHz signal. I set my SSID to be different for 5GHz (NETWORK vs NETWORK-5G for example). Then, on devices that support 5GHz, I program the 5G SSID but not the 2.4 SSID. This leaves the 2.4 range for the few devices that cannot use the 5GHz.
Also, if you do see neighbor's networks, determine which channel they use and manually set your channels to be different rather than accept "automatic". If you can, avoid channel 6 on the 2.4 frequency which is right in the middle of the spectrum and most susceptible to interference.
If the range is poor in parts of the home, consider an additional access point such as Airport Express. If you can, connect this via Ethernet to the main router and set the WiFi up identical to the router to allow you to freely roam without switching networks. If ethernet is a challenge, consider MOCA or Ethernet over Powerline adapters to use house Coax (MOCA) or power lines to transmit the data to a remote location. If you go this route, don't skimp as older technologies were pretty slow.
I have had a Time Capsule AC for several years and experience no slow downs, in fact my ISP keeps raising my service level and my speeds increase every time they do. I added an older AP Extreme and AP Express via ethernet and power line and am able to connect to 5G band anywhere in my home with speeds equal to my ISP service (currently about 70Mbps). I also took the time to tune my channels so the Airport devices use different channels that don't overlap, and avoid sharing channels with neighbors WiFi.
You may be able to improve your network speeds at little or no cost by doing some of these steps.