I have that battery I use around the garage when I need 12v DC power. It's been a good battery.
When you say you're expecting 5 amps total what does that mean? You have a draw of 5 amps when every thing is running? Or 5AH in a 24 hour period? Big difference. Know which will help.
I'm planning the average daily draw for me will be around 15AH in 24 hours. So I would need a 30AH battery, because you really don't want to discharge lower than 50%. And that would be for just one day and the battery would have to be recharged.
You will find that the cost different per AH does not vary much from a 7AH battery to a 400AH battery. It will be from about $2.00 per AH up to $3.00 per AH the higher price is for premium brands. And weight works the same way. There is no free lunch as they say. The big monkey wrench in all this is lithium deep cycles. When you compare the stats of lead vs lithium it is a no brainer, lithium wins out. But at $9.00 to $12.00 per AH that is hard to do. I'm looking at a 75AH lithium battery for $700.

I talk myself in to get it and out a few times a day.
Todd