iPhones will slow down over time, components wear out, and storage and memory fill up with old files and forgotten apps.
Below are a few simple things you can do to help speed things up:
From time to time you should power off your device. This clears out the memory.
You should also get into the habit of deleting apps and files you don't use regularly and archive the latter in cloud and/or local backup. Head to Settings > General > Storage & iCloud Usage and select Manage Storage under the Storage section. Here, you'll see a chart that shows you how much space you are using and how much free space you have remaining.
It's also worth going through the settings and checking which apps refresh in the background, thereby using up precious processing power.
Update iOS on your device.