<s>[INST] Prove $5^n +5 <5^{n+1}$ $∀n∈N$ using induction Prove $5^n +5 <5^{n+1}$ $∀n∈N$
Base Case: $n=1$
$\implies 5^1 +5 <25$
$\implies 10<25$ ; holds true
Induction hypothesis: Suppose $5^k +5 < 5^{k+1}$ is true for k∈N
Then;
$\implies 5^{k+1} +5 < 5^{k+2}$ 
$\implies 5\cdot 5^k +5 < 25*5^k$
I don't know how to proceed after this step.
 [/INST] $$5^{k+1}+5=5\times 5^k+5<5(5^{k+1}-5)+5=5^{k+2}-25+5<5^{k+2}$$
Notice that, by the induction step, we have $$5^k+5<5^{k+1}\implies 5^k<5^{k+1}-5$$
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