At 5A I wouldn’t even be charging at 1c. Most hobby lipos are rated to at least 1c charging and many can take much more. I occasionally charge my multirotor lipo’s at 2-3c and have 100’s of cycles with little damage to the batteries. Some of the packs I own are rated to 5c charge rate. I like my house in its unburnt state so I would not push to 5c.
My batteries are also rated for 5C charge but I charge them at 1C. Fast enough for my recreational riding.
The power supply in the article you posted shows specs with CC/CV output but I didn’t see that in the power supply you listed.