Only having an empire of 5 planets concern me. R u playing on a small map. If u r thats cool since I don't play on small maps, and don't have any idea on this. But if u r not playing on a small map. Then u r doing something wrong. Hope u r not making the mistake of self suficient economies. Some people freak out if they can't have a production of %100. The truth is the game requires this. This is the way that your population grows. It does appear that u r colonising faster, but in reality u will go bankrupt and not be able to colonise without lowering production to increase approval. the higher the approval the faster your taxes grow. The more influence you get. This also affects tourism. When U get more money, and get better morale improvements u will be able to increase production and raise taxes. This will keep u from turning the galactic version of Haiti. I don't think u r trying to be the weakest species on the game.
Don't feel like u have to save money. U r not playing this game for points anyways right. If u were don't u think it would be better applied by what u build, production, military, tactics, and research. This is a good reason to not worry about building money. It looks good, but don't help u build a civilization.
U start out the game with a survey ship. Instead of manually controlling the ship or putting the ship on auto explore u should make sure to put your ship on auto survey. I would recommend researching sensors as soon as possible. Then u need to dedicate a planet to producing sur advice research sensors and when u get the chance convert one planet to produce survey ships. I would recommend cargo hulls. They r big cheap ships. It would be counter productive to arm these, so the hit points don't matter. This might get u a lot of extra money early on.
I don't think it is a mistake to build factories in the colony rush. U can always build over them later. U need to pay attention to your economics. I don't like planets with a pq lower than 10, but grab them anyway. Matter of fact grab as many planets as possible. It will take time, but this will give u more money in the end through taxes and tourism from influence. The more people u have the more u have. Remember the more colony ships u have the more colonies u have the more population u have. Unless u find resources. Be careful u don't want to dedicate to much of your production. This takes u away from making colonies. Til at the end of the colony rush.
The first structure u build should be starports. It does become helpful if u make the ships as best as possible. I'm weird I like factories. A lot of people don't like to be over industrialised. I think is caused because they don't have their approval high enough or doesn't have a good enough economic stradegy. After U build your factories buidl morale structures. If u r the Krynn research temples and healing pools for the torians. The reason I'm saying this is because they start off with really expensive morale structures. The Torians at least have entertainment network, so I would at least buid this until I have healing pools. Until then I would build a consolate and then research labs until I have the Temple of Krynn if I'm the Krynn. If I'm the torians I have the market centers instead until my spending is more than my income. If my income is more then I would build schools instead.
At this point u have to decide on what u r doing. From what I know there r 2 ways to go about things at this point. Unless I'm the Yor I use only one, but if u like the other way u can do it that way. If u r the Yor u can trade or steal techs to do it the other way. Some races start out without economic structures or only use one per planet causing them to go the farming stradegy. Some races start out with farming or economic structures. Some can research them others can't. If your expense is more that your income build economic structures otherwise build research structures. If u would rather or if u r the Yor u have to pick a different stradegy. The stradegy is a farming one. The more population u have the more taxes and tourism u have. This might not work very good if your unit is a one per planet farming unit or u don't start out with a farming unit. U may need to research, trade for, or steal a farming tech. U also need to have the appropriate morale tech. If your morale is above %51 u can build a farm. Remember farms work better at raising the population than a population raising unit. Personally I never had a problem raising my population above 20 billion, but they advise against raising your population above 20 billion per planet. They say this causes a serious morale problem. If U have the economic structures u can augment this with economic units.
Terraform when your population is under 1 billion under the maximum population limit. Start researching farming techs. Then build a farm. Do that each time u reach the maximum population limit. Until u can't research no more farming techs. Remember don't let your planets population exceed 20 billion. Some of your planetary artifacts will change how u run the planet. If it is a starship or production planets then go all factory. This may cause your approval, production, or taxes to be lower though. U might to do the same for research.The only exception is your technology capital. Find the biggest planet u can find to make it your technology capital. Your home planet will make a good economic and political capital; because, it starts out with more population. When u build wonders go to your colony screen, and find the one with the most social production. Build the wonder on this planet concentrating on social production.