5 minutes is 300 seconds so I just did a ping test and I got 2 ms as the max ping and 0 ms average with 300 times ping to router. I don't turn off my "desktop replacement" (doesn't even have the 1/3 processing power of a true desktop) laptop unless it has updates from Windows or I needed to perform my laptop cleaning so it just stays connected for about 15 days max without ever dropping the WiFi. I just use a cheap $25 refurb Netgear WNDR3400v1 from Amazon and it amazingly performs well though throughput is limited to 90 - 95 Mbps due to fast Ethernet.
It might just be your router is prioritizing your other laptops with QoS management though ping spikes to 250 ms is a concern. DPC latency can also cause those spikes so you try troubleshooting starting from there as well.