I would like to add a few things here. The 3.7 volts is the nominal voltage of a lipo cell. 4.2 volts is the maximum voltage, so the charger should actually be bringing each cell up to 4.2 volts to get a full charge.
Charging at 5 amps is safe I would say and here's why. With lipos we have something called c rating, which is kinda a way to measure charge/discharge rate based on the capacity of the lipo. For example, 1C is the battery's capacity, or in your case 5.2 amps (5200 mAh = 5.2 amps). If the max discharge rate of the pack is 25C for example, you can safely draw 130 amps from the pack because 5.2 amps x 25C is 130 amps. Now normally you can discharge at much higher than 1C safely, and most times you will be pushing way past that, that isn't an issue and is normal. When it comes to charging though, it is not recommended to go past 1C (5.2 amps in your case). The manufacturer might say that you can do 2C, 5C, or whatever else, but it is generally advised to stay at 1C or below.
If you charge at 1C (5.2 amps for a 5200 mAh pack), it should take about an hour to charge, but some chargers (like mine) take much longer, closer to 90 minutes, because the charger slows down the charge rate near the end of the charge and gets ready to stop charging.
When somebody told you to stay below 0.5A charge rate, it is probably because some people set a maximum charge rate for themselves, regardless of battery capacity. Some won't pass 1 amp, and whoever told you to stay below 0.5 obviously has set their limit to 0.5. I personally just charge at 1C, but my packs usually aren't very big like yours is. I would recommend sticking to 5 amps for charging, and maybe going down a little bit more in charge rate just to be safe (as low as you have the patience for really). You could go to a lower charge rate like 1 amp, but it will take over 5 hours at 1 amp so I'm guessing you don't want to do that. I did say that I stick to 1C, but your pack is larger and usually larger packs are scarier and more dangerous, so you want to be extra careful with them, so the extra level of precautions is a good thing here.
Now a few general charging tips:
1. NEVER leave a charging lipo unattended. Things happen quick with lipo fires, so you don't want to leave it alone while charging (arguably when it has the highest chance of lighting on fire other than when it is damaged).
2. It is hard to put out a lipo fire, I have heard that sometimes fire extinguishers aren't super good at it. A fire extinguisher will most likely work, but the best method that I know of to stop a lipo fire is to cover it with sand. I personally keep a container of sand next to the charging setup while charging so that I am always ready.
3. Things like battery bunkers are great for safe charging. There are even designs that will automatically douse the lipo in sand if there is a fire. You can make one yourself and it shouldn't cost too much. (I will put a video on battery bunkers at the end of the post)
4. If you don't have a battery bunker right now, then at least charge the lipo inside of a lipo bag, it will provide some level of protection.
The battery bunker video:
Any questions will be welcome, and stay safe with your lipos!