That 5% sounds like a number pulled from the air to be honest. I don't think it will damage the battery if you deplete it fully. I have done it once since I've had it (five days) because the battery on mine seems to last so long (not complaining! Old iPhone wanted charging three times a day) I struggle to fully deplete it before a reasonable hour. Had 12% at 11pm last night, the other half had to be up for work at 4am so I thought I won't put it on charge until then as hopefully it will be flat. Wrong. 8% so stuck it on charge.|
What I do suggest is that you turn the phone off whilst it's charging as it not only results in a quicker charge but the phone can tell when it's fully charged better,