my parents think that something professional is better than something homemade.
This is not true. What matters is that it meets the chickens' needs. The chickens won't care if it's professional or DIY, if it's pretty or ugly. People fall for the professional trap often, order these beautiful coops made by carpenters, that are inadequate for chickens, because the profession in question is carpentry - how to build things - not chicken keeping, and those carpenters don't have a good understanding of the chickens' needs. Those beautiful coops are often very poorly ventilated, and advertise being able to fit way more chickens than is appropriate for that size. So, just because a professional carpenter built it, and said you can stuff three dozen chickens in it, doesn't mean that that's a good setup... Same with the Eglu. The Eglu is not even professional. It's a commercial product meant to sell and make money, and the people who make it aren't after the chickens' wellfare, they want to make it cute and convenient and appealing to the buyer. A coop can be the ugliest DIY in the world, but if it meets the chickens' needs and keeps them healthy and happy, then it's absolutely better than the prettiest thing you can buy premade.
But as to them being a piece of crap, I have heard that they are actually pretty good, from here and other places, just not big enough for what they say.
People swear by all kinds of less-than-optimal things. People have different experience levels and knowledge levels, and each situation is different. But serious chicken keepers with knowledge and experience would not recommend an Eglu, for many reasons not just the size.
Would you be able to direct me to an easy coop that is big enough for them?
Your thought about converting a shed is in the right direction. Often sheds make much better coops than actual coops sold as such - they tend to be cheaper (or maybe you have one already), there's more variety in terms of size, and you can modify it to fit your needs. So a converted shed is actually a great idea! Just keep in mind the minimum recommended space of 4 square feet per chicken in the coop. 5x3 would still be too small for the number and size of chickens you want. Once you add roosts and nesting boxes, there will be barely enough room for the chickens to pass each other without stepping on each other or getting into each other's personal space. If they are packed too tight, they start fighting. Chickens are mean animals that guard their personal space and their pecking order. See if you can find a bigger shed, one that will allow them at least 4 square feet, in addition to the roost and nesting boxes. Prevention is better than treatment - better set yourself up for success, so you'll have an easier time later, than end up having to deal with preventable problems like conflict and pecking, sanitation issues, ammonia buildup and the other problems associated with spaces that are too small.