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You didn't say what tank you noticed this slime in. I am assuming it is the coolant reservoir?
If so, the slime could be 1 of 2 things:
1. Dirty antifreeze. Antifreeze contains cleaners that degrade over time. This is why it is recommended to change the coolant at recommended intervals - not because it won't cool any more, but because the detergents degrade and can no longer clean. To remedy this, you will need to drain, flush and refill the cooling system. Not doing so can result in a clogged radiator.
2. Oil in the antifreeze. This can be the result of several things, such as a cracked head, cracked block, or blown head gasket. Any of these will usually also result in antifreeze in the oil. This will be evident by a white foamy color of the oil.
The old, dirty antifreeze is the most likely culprit. Flush the cooling system and change the antifreeze. If this does not help, you will need to have the engine pressure tested to check for cracks.