Python 3, 97 bytes

f=lambda t,a,*p:t==0<len(p)==5and{p}or{i for v in[*a]for i in f(t-a.pop(0),[*a],*sorted([*p,v]))}

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Input target value and the array of nums, output a set of tuples.

Python 3, 95 bytes

f=lambda t,a,*p:[p][t*t:len(p)==5]or{i for v in[*a]for i in f(t-a.pop(0),[*a],*sorted([*p,v]))}

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Input target value and the array of nums, output a set of tuples.

Python 3, 100 bytes

f=lambda t,a,*p:t==0<len(p)==5and{p}or{*sum([[*f(t-a.pop(0),[*a],*sorted([*p,v]))]for v in[*a]],[])}

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Python 3, 97 bytes

f=lambda t,a,*p:t==0<len(p)==5and{p}or{i for v in[*a]for i in f(t-a.pop(0),[*a],*sorted([*p,v]))}

Try it online!

Input target value and the array of nums, output a set of tuples.