Will replacing my 5 year old internet router increase my internet connection?

[DunbarPappy®ϟϟ]

Stop guessing.
Test your Internet services after you've verified all the incoming connections are clean and secure.

Test all your relevant network stats, but pay particular attention to "network buffer measurements" to see what it is:
ICSI Netalyzr: http://netalyzr.icsi.berkeley.edu/
Requires JavaScript. NoScript users can 'temporarily allow berkley...'
This takes several minutes to run.

The results will give the entire Network, which includes your ISP, so although your router may be just fine, it could be the ISP config's that are mis-adjusted or could be tweaked. Many's the time a person complains to the ISP, and they flatly deny any responsibility, without actually examining their configs.
Also gives some solutions, based on your results.
----------
And ;
https://www.grc.com/dns/dns.htm
Read what it does and how it works.